Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 376375 9 pageshttpdxdoiorg1011552013376375

Research ArticleUsing the Fuzzy Linguistic Preference RelationApproach for Assessing the Importance of Risk Factors ina Software Development Project

Shih-Tong Lu12 Shih-Heng Yu2 Dong-Shang Chang2 and Shih-Chang Su2

1 Graduate Institute of Project Management Kainan University No 1 Kainan Road Taoyuan Luzhu Shiang 33857 Taiwan2Department of Business Administration National Central University No 300 Jhongda Road Taoyuan Jhongli City 32001 Taiwan

Correspondence should be addressed to Shih-Tong Lu stonelu8604gmailcom

Received 15 January 2013 Accepted 28 April 2013

Academic Editor Ker-Wei Yu

Copyright copy 2013 Shih-Tong Lu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This study employs fuzzy linguistic preference relation (Fuzzy LinPreRa) approach to assess the relative degree of impact ofrisk factors in software development project for two expert groups working in technology enterprises and software developmentcompanies For the identified risk dimensions the results show the same rankings for these two groups ldquoOrganization functionriskrdquo is considered the most important dimension influencing the software development project performance with the othersin order being ldquodeveloping technology riskrdquo ldquoresources integration riskrdquo ldquopersonnel system riskrdquo and ldquosystem requirement riskrdquoThe proposed approach not only facilitates the information collecting for making pairwise comparisons but it also eliminates theinconsistencies in the collected information

1 Introduction

Software development projects are usually designed by highlyskilled and trained experts due to projectsrsquo complicateprofessional and technicality nature However these typesof projects often have series of setbacks such as high costschedule overruns quality issues and usability problems [12] From the past experience most software developmentprojects use more resources than originally planned takelonger time to complete and unfortunately often deliverpoor functionality and low quality than expected [3] It isobvious that the life cycle of software development process isinherent numerous uncertainties and risk factors Thereforethere are some researchers that focused on the study of riskevaluation risk assessment and riskmanagement of softwaredevelopment

Since there are numerous risks in software developmentthe proposed assessment procedure has designed using mul-tiple criteria decision making (MCDM) approach Besidesassociated risk evaluation is often determined by expertssubjectively however it is not easy for the experts to achieveprecise judgments with limited time Therefore to solve the

problem of incorporatingmore assessment factors and work-ing within time limitations for interviews with experts thisstudy applies the fuzzy linguistic preference relation (FuzzyLinPreRa) proposed by Wang and Chen [5] This method isbased on the consistent fuzzy preference relations (CFPRs)approach which was proposed by Herrera-Viedma et al[6] to deal with the relative degree of impact of softwaredevelopment risk factors The results can provide decisionmakerswith the ability to propose riskmanagement strategiesin advance of implementing a software development project

2 Risk Factors for a SoftwareDevelopment Project

Many uncertain problems could confront whether done byoneself or by outsourcing groups when the software develop-ment projects are performed In order to reduce failure rateof software development software engineers and informationsystem researchers should always identify asmany risk factorsaffecting project outcome as they can In the literaturesreview ten risk items for software development projects

2 Mathematical Problems in Engineering

were identified by Boehm [7] which include personnelshortfalls unrealistic schedules and budgets developingthe wrong functions and properties developing the wronguser interface adding more functionalityfeatures continualrequirement changes shortfalls in externally furnished com-ponents shortfalls in externally performed tasks real-timeperformance shortfalls and straining of computer-sciencecapabilities A hierarchical structure model for evaluatingsoftware development risk was constructed via fuzzy settheory by Lee and Lin [8] They proposed six risk attributesin order to evaluate the aggregative risk personnel systemrequirements schedules and budgets developing technologyexternal resource and performance The fourteen risk itemscan be categorized into six attributes

The twelve risk categories identified by Jiang andKlein [9]include technological acquisition project size lack of generalteam expertise lack of teamrsquos expertise with the task lack ofteamrsquos development expertise lack of user support intensityof conflicts extent of changes brought resources insufficientlack of clarity of role definitions application complexityand lack of user experience In addition Houston et al[10] listed thirty software development risk factors andfurther studied the effects of six common and significant riskfactors They are creeping user requirements lack of staffcommitment lowmorale instability and lack of continuity inproject staffing inaccurate cost estimation excessive sched-ule pressure and lack of senior management commitmentBuyukozkan and Ruan [11] applied the Choquet integralaggregation approach to analyze the effects of importanceand interactions among software development risks Theyextracted software development risk factors by surveying alarge amount of literature and they explored several typesof risks including product engineering risks developmentenvironment risks and program constraint-related risks suchas the main risk dimensions Factors associated with productengineering risks include requirements design code and unittests integration and testing engineering specialists Fac-tors in development environment risks include developmentprocess development system management process manage-ment methods and work environment Resource contractand program interfaces are those factors that influence theprogram constraint risks Lu and Ma [12] identified the riskfactors according to the life cycle of a software developmentproject for owners and contractors For owners the causes ofrisk are distinguished into conceive stage development stageexecution stage and finish stage In the conceive stage anddevelopment stage there are eight risk factors respectivelySix risk factors belong to execution stage but in finish stagethe main risk factor is that there is no standard and criterionof the information system For contractors risk factorsin software development include four aspects policy risktechnique risk scope change risk and management risk Themanagement risk consists of cost management risk qualitymanagement risk schedule management risk integrationmanagement risk human resources management risk andcommunicationmanagement risk Lu and Yu [4] constructeda hierarchical structure of five dimensions and associatedtwenty-two risk factors for software development project and

presented two approaches to assess the importance and theranking of these risk factors by fuzzy set theory The five riskdimensions include organization function risk developingtechnology risk personnel system risk resources integrationrisk and system requirement risk

From these literatures review the software developmentrisk factors were further screened and synthesized for thisstudy We can adopt the hierarchical structure of risk factorsdeveloped by [4] for applying the proposed Fuzzy LinPreRaapproach conveniently Figure 1 shows the hierarchical struc-ture of risk factors for a software development project

3 Method for Assessing the Degree ofImpact of Risk Factors

This study not only would like to realize the risk factors inthe process of software development but is also considerswhich of these factors are important for the projectmanagersIt is impractical to assume that the different project riskfactors equally affect project success Therefore the impactdegree of the risk factors on project success should becarefully evaluated for bettermanaging of the project risk andincreasing the chance of project success That is the varyingeffects of project risk factors on project success provide valu-able information needed to allocate software developmentproject resources This study would like to assess the relativeimpact degree among software development risk factorsfor helping developers to draw up the risk managementstrategies However the largest possible number of evaluationcriteria of a dimension is five If we apply the conventionalanalytic hierarchical process (AHP) proposed by Saaty [13]or fuzzy AHP proposed by Buckley [14] to design the ques-tionnaire we may encounter great difficulties and challengesin collecting information In addition the model also needsto consider the fuzziness of the judgments or opinions ofselected experts when they answer the questionnaires Thusthis study applies the fuzzy linguistic preference relation(Fuzzy LinPreRa) approach for constructing the decisionmatrices of pairwise comparisons The FLPR approach wasconstructed by Wang and Chen [5] based on the consistentfuzzy preference relations (CFPRs) proposed by Herrera-Viedma et al [6] The Fuzzy LinPreRa not only makes it easyfor interviewers to use linguistic variables to present a setof criteria with the least amount of subjective judgment butit also avoids the necessity to check for consistency in thedecision-making process More importantly it is more con-venient to acquire the judgments of practitioners or expertsof software development industry through a questionnaire Abrief introduction of the definitions and steps in the adoptedFuzzy LinPreRa method is given

31 Consistent Fuzzy Preference Relations (CFPRs) The fuzzypreference relation 119875 on a set of evaluation criteria 119883 isa fuzzy set of the product 119883 times 119883 with a membershipfunction 119875 119883 times 119883 rarr [0 1] The preference relation isrepresented by the 119899 times 119899 matrix P = [119901

119894119895] where 119901

119894119895=

119875(119909119894 119909119895) for all 119894 119895 isin 1 119899 Herein 119901

119894119895is interpreted as

the degree of importance of criteria 119909119894over 119909

119895 If 119901119894119895= 05 it

Mathematical Problems in Engineering 3

Softw

are d

evelo

pmen

t risk

organization function risk

developing technology risk

personnel system risk

resources integration risk

system requirement risk

continuing stream of requirements changeslarge number of complex user interfacesdeveloping the wrong software functionadding more functionalityfeatures

lack of contact personrsquos competencein coordination with related divisionslack of quantitative historical datashortfalls in externally furnished components

reliance on a few key personnelunavailability of key staff or project managerlack of staff experience and technologylack of staff commitment and low morale

inexperience with the user environmentoperation

immature developing technologylow productivity in developing technologystraining software and hardwareinadequate scheduling and cost estimation

incapable organization managementinadequate scale of organization

lack of organizational maturity

instability and lack of continuity in project staffing

lack of communication channel in organization

F1

F2

F3

F4

F5

F11F12F13F14

F21F22F23F24

F31F32F33F34F35

F41F42F43F44

F51F52F53F54F55

Figure 1 Hierarchical structure of risk factors for a software development project [4]

means that 119909119894and 119909

119895are equally important119901

119894119895= 1 indicates

that 119909119894is absolutely important to 119909

119895 and 119901

119894119895gt 05 shows

that 119909119894ismore important than 119909

119895 In this case the preference

matrix P is usually assumed to be additive reciprocal thatis 119901119894119895+ 119901119895119894= 1 for all 119894 119895 isin 1 119899 When the reciprocal

fuzzy preference relation P = [119901119894119895] is consistent and verifies

additive consistency there exists a relationship equation suchthat [6]

119901119894(119894+1)

+ 119901(119894+1)(119894+2)

+ sdot sdot sdot + 119901(119895minus1)119895

+ 119901119895119894=(119895 minus 119894 + 1)

2

forall119894 lt 119895

(1)

Equation (1) is very important because it can be usedto construct a consistent fuzzy preference relation from theset of 119899 minus 1 values 119901

12 11990123 119901

(119899minus1)119899 If a decision matrix

with entries in the interval [minus119886 1 + 119886] 119886 gt 0 is outsidethe interval [0 1] it can be constructed by transforming theobtained values using a transformation function that pre-serves reciprocity and additive consistencyThe transformingfunction is 119891 [minus119886 1 + 119886] rarr [0 1] 119891(119909) = (119909 + 119886)(1 + 2119886)In such a way we can facilitate the expression by the evaluatorof consistent preferences in the decision process

32 Linguistic Variables and Fuzzy Numbers A linguisticvariable is the one whose values are words or sentences

expressed in a natural or artificial language Here we usethis kind of expression to compare the impact degree oftwo risk dimensions or factors for a software developmentproject using linguistic terms ldquoabsolutely (not) importantrdquoldquovery strongly (not) importantrdquo ldquoessentially (not) importantrdquoldquoweakly (not) importantrdquo ldquoequally importantrdquo with respectto a triangle fuzzy number (TFN) proposed by [15] A TFNis a fuzzy number on R if its membership function 120583

(119909)

R rarr [0 1] is equal to (2) following the definition in [14]

120583(119909) =

(119909 minus 119897)

(119898 minus 119897) 119897 le 119909 le 119898

(119906 minus 119909)

(119906 minus 119898) 119898 le 119909 le 119906

0 otherwise

(2)

where 119897 and 119906 stand for the lower and upper bounds of thefuzzy number respectively and 119898 stands for the medianvalue The TFN can be denoted by = (119897 119898 119906) and Table 1shows the corresponding TFN for each linguistic assessmentvariable The table of converting linguistic terms to fuzzynumbers is constructed from [15] Detailed conversion scalescan contain andmatch all the verbal terms given by the evalu-ators and it is very important for the evaluators to be familiarwith the decision problem context

4 Mathematical Problems in Engineering

33 Fuzzy Linguistic Preference Relations (Fuzzy LinPreRa)Given a set of criteria 119883 = 119909

1 119909

119899 is associated with

the fuzzy linguistic preference relations matrix P = [119901119894119895] =

(119901119897

119894119895 119901119898

119894119895 119901119906

119894119895) based on consistent fuzzy preference relations

and fuzzy linguistic assessment variables If the matrix abovecomplies with additive reciprocal consistency then the fol-lowing statements must be equivalent

119901119897

119894119895+ 119901119906

119895119894= 1 forall119894 119895 isin 1 119899

119901119898

119894119895+ 119901119898

119894119895= 1 forall119894 119895 isin 1 119899

119901119906

119894119895+ 119901119897

119894119895= 1 forall119894 119895 isin 1 119899

119901119897

119894119895+ 119901119897

119895119896+ 119901119906

119896119894= 15 forall119894 119895 isin 1 119899

119901119898

119894119895+ 119901119898

119895119896+ 119901119898

119896119894= 15 forall119894 lt 119895 lt 119896

119901119906

119894119895+ 119901119906

119895119896+ 119901119897

119896119894= 15 forall119894 lt 119895 lt 119896

119901119897

119894(119894+1)+ 119901119897

(119894+1)(119894+2)+ sdot sdot sdot + 119901

119897

(119895minus1)119895+ 119901119906

119895119894=(119895 minus 119894 + 1)

2forall119894 lt 119895

119901119898

119894(119894+1)+ 119901119898

(119894+1)(119894+2)+ sdot sdot sdot + 119901

119898

(119895minus1)119895+ 119901119898

119895119894=(119895 minus 119894 + 1)

2forall119894 lt 119895

119901119906

119894(119894+1)+ 119901119906

(119894+1)(119894+2)+ sdot sdot sdot + 119901

119906

(119895minus1)119895+ 119901119897

119895119894=(119895 minus 119894 + 1)

2forall119894 lt 119895

(3)

Notably if the values of the obtained matrix P withelements in the interval [minus119888 1 + 119888] (119888 gt 0) are not in theinterval [0 1] the obtained fuzzy numbers will need to betransformed by way of a transformation function to preservethe reciprocity and additive consistency The transformationfunctions for left median and upper values of TFN in everyelement of decision matrix P are given in (4) Finally we canobtain a consistent additive reciprocal decision matrix P1015840

119891 (119909119897) =

(119909119897+ 119888)

(1 + 2119888)

119891 (119909119898) =

(119909119898+ 119888)

(1 + 2119888)

119891 (119909119906) =

(119909119906minus 119888)

(1 + 2119888)

(4)

34 Determination of Criteria Weights If there are 119898 eval-uators to participate in the judgments this study uses thenotion of the average value to integrate the fuzzy judg-ment values of 119898 evaluators from the set of 119899 minus 1 val-ues 119901

12 11990123 119901

(119899minus1)119899 that is

119901119894119895= (

1

119898) otimes (119901

1

119894119895oplus 1199012

119894119895oplus sdot sdot sdot oplus 119901

119898

119894119895) (5)

Here we can establish an original synthetic fuzzy judg-ment matrix P and then use (3) and (4) to obtain the con-sistent synthetic fuzzy judgment matrix P1015840 In order to obtain

Table 1 Fuzzy linguistic assessment variables

Linguistic variables Triangle fuzzy numbersAbsolutely important (AB) (090 100 100)Very strongly important (VS) (080 090 100)Essentially important (ES) (050 070 090)Weakly important (WK) (050 060 070)Equally important (EQ) (040 050 060)Weakly not important (WN) (030 040 050)Essentially not important (EN) (010 030 050)Very strongly not important (VN) (000 010 020)Absolutely not important (AN) (000 000 010)

Table 2 Original evaluation results for the risk dimensions by thefirst group

E1 E2 E3 E4 E5

F1 VS VS EQ WN VN F2

F2 VN VS EQ AB AB F3

F3 VS VN WN VS VN F4

F4 EQ EN VS WK EQ F5

the weights of each criterion this study adopts column vectoraverage approach proposed by Saaty and Vargas [16] asfollows

119903119894119895=

119901119894119895

1199011119895oplus 1199012119895oplus sdot sdot sdot oplus 119901

119899119895

119908119894=1

119899(1199031198941oplus 1199031198942oplus sdot sdot sdot oplus 119903

119894119899) = (119908

119897

119894 119908119898

119894 119908119906

119894)

(6)

The result of the fuzzy synthetic decision reached byeach criterion is a fuzzy number (119908119897

119894 119908119898

119894 119908119906

119894) Therefore it

is necessary that a defuzzification method for fuzzy numbersis used Methods for such defuzzified weighting generallyinclude the mean of maximal (MOM) center of area (COA)and 120572-cut methods [17 18] This study utilizes the COAmethod to find that the nonfuzzy value is a simple and practi-cal methodThe defuzzified weights of the fuzzy number canbe found by the following equation

119908119894=

(119908119897

119894+ 119908119898

119894+ 119908119906

119894)

3forall119894 (7)

4 Case Study

Two companies were invited to answer the questionnairerelated to the risk of a software development project Thefirst group is comprised of five experts with 5 to 15 yearsrsquoexperience in the information management division from amedium scale technology enterpriseThe second group is alsocomprised of five experts with 5 to 10 yearsrsquo experience inestablishing enterprise resource planning (ERP) systems fora software development company The individuals in the twogroups were invited to provide responses to the questionnaire

Mathematical Problems in Engineering 5

Table 3 Original evaluation results for the risk dimensions by thesecond group

E1 E2 E3 E4 E5

F1 ES VS VN WK EQ F2

F2 EQ WN VS VS VS F3

F3 ES VS EN AN WN F4

F4 ES WK EQ AB WK F5

Table 4 Original evaluation results for the risk factors by the firstgroup

E1 E2 E3 E4 E5

1198651

F11 VS AB VS EQ AB F12

F12 VN VN VN ES EN F13

F 13 AB WK EQ ES WK F14

1198652

11986521

VS AB VS WK ES F22

11986522

VS EQ WK WK EN F23

11986523

AN VN EN EQ VN F24

1198653

F31 AN VN EQ VN AN F32

F32 VS VS WK VN AB F33

F33 AN AN VN AN VS F34

F34 EQ VS AB EQ VN F35

1198654

F41 EQ EN EQ WN EQ F42

F42 VS VN VN ES VS F43

F43 EQ ES WK VS WN F44

1198655

F51 VS AB AB VS ES F52

F52 EQ VS WN VN EN F53

F53 EQ VS ES ES ES F54

F54 VS VN WK VS EQ F55

survey and were asked to compare the relative degree ofimpact for the risk dimensions and factors identified inthis study in pairwise sequential order That is they onlyneeded to compare the relative impact degree from 119865

1to

1198652 from 119865

2to 1198653 from 119865

3to 1198654 from 119865

4to 1198655 from 119865

11

to 11986512 from 119865

12to 11986513 and so on Tables 2 and 3 list the

original evaluation results of this pairwise comparison for therisk dimensions given by the five experts of the two groupsSimilarly Tables 4 and 5 display the original pairwise compar-ison matrix for the twenty-two risk factors given by the twogroups Since the preferences and experiences of these expertsare different we use the fuzzy linguistic assessment variablesas in Table 1 and from (3) to (5) to aggregate the expertsrsquosubjective judgments toward the impact of the degree of riskdimensions and factors yielding the synthesized triangularfuzzy numbers listed in Tables 6 7 8 and 9 respectively Theranking of the impact degree is determined by constructinga crisp value from the fuzzy number Hence defuzzificationneeds to be performed to arrange the fuzzy numbers for

Table 5Original evaluation results for the risk factors by the secondgroup

E1 E2 E3 E4 E5

1198651

F11 VS ES EQ VS WK F12

F12 WN EN EQ VN EN F13

F13 ES ES EQ VS ES F14

1198652

F21 WN EN EQ AB WN F22

F22 ES ES VS VS VN F23

F23 EN VN AN AN EN F24

1198653

11986531

ES VS VN AB VS F32

11986532

ES WK VS AB VN F33

11986533

WN EN EQ AN EQ F34

11986534

ES ES EQ AB EQ F35

1198654

F41 WK ES EQ AN WK F42

F42 ES ES ES VS EQ F43

F43 ES ES EQ VS WK F44

1198655

F51 VS VS AB AB ES F52

F52 EQ EN EQ VS WN F53

F53 EQ ES EQ VS ES F54

F54 EN EN VN EN WN F55

ranking Table 10 lists the impact degree and ranking of riskdimensions and factors for software development projectsobtained by using (6) and (7)

For experts in the first group who are staff members of atechnology enterprise among the identified five dimensionsldquoorganization function riskrdquo was found to be the mostimportant risk dimension to influence software developmentperformance and success ldquoDeveloping technology riskrdquo andldquoresources integration riskrdquo are respectively the second andthird highest impact dimensions affecting software devel-opment project performance ldquoPersonnel system riskrdquo andldquosystem requirement riskrdquo are the last two dimensions insequence in relative importance affecting performance andsuccess of the software development project

For each dimension among the first risk dimensions (1198651)

incapable organizationmanagement (11986511) was considered the

most impact risk factor and it is also the most importantfactor for the global aspect Among the second fourth andfifth dimensions (ie 119865

2 1198654 and 119865

5) immature technology

development (11986521) improper coordination with related divi-

sions (11986542) and continuing stream of requirements changes

(11986551) were all found to be the highest impact risk fac-

tors influencing the software development project successUnavailability of key staff or project managers (119865

32) and

lack of staff commitment and low morale (11986534) respectively

are the most observed prominent risk factors which harmsoftware development project success in each dimension

The points of view in relation to the risk dimensionsexpressed by the experts of the second group who are staff

6 Mathematical Problems in Engineering

Table 6 Aggregation decision matrix of the risk dimensions form the first group

1198651

1198652

1198653

1198654

1198655

1198651

(050 050 050) (047 054 062) (054 069 081) (046 068 087) (041 072 100)

1198652

(038 046 053) (050 050 050) (057 065 069) (049 063 075) (044 068 088)

1198653

(019 031 046) (031 035 043) (050 050 050) (041 049 056) (037 053 069)

1198654

(013 032 054) (025 037 051) (044 051 059) (050 050 050) (046 054 063)

1198655

(000 028 059) (012 032 056) (031 047 063) (037 046 054) (050 050 050)

Table 7 Aggregation decision matrix of the risk factors from the first group

1198651

11986511

11986512

11986513

11986514

11986511

(050 050 050) (072 080 085) (040 060 077) (045 075 100)

11986512

(015 020 028) (050 050 050) (018 030 042) (023 045 065)

11986513

(023 040 060) (058 070 082) (050 050 050) (055 065 073)

11986514

(000 025 055) (035 055 077) (027 035 045) (050 050 050)

1198652

11986521

11986522

11986523

11986524

11986521

(050 050 050) (066 076 084) (063 082 100) (031 058 085)

11986522

(016 024 034) (050 050 050) (047 056 066) (015 032 052)

11986523

(000 018 037) (034 044 053) (050 050 050) (018 026 035)

11986524

(015 042 069) (048 068 085) (065 074 082) (050 050 050)

1198653

11986531

11986532

11986533

11986534

11986535

11986531

(050 050 050) (018 023 030) (026 038 052) (000 015 036) (000 023 050)

11986532

(070 077 082) (050 050 050) (058 065 071) (032 042 056) (032 050 070)

11986533

(048 062 074) (029 035 042) (050 050 050) (024 027 035) (024 035 048)

11986534

(064 085 100) (044 058 068) (065 073 076) (050 050 050) (050 058 064)

11986535

(050 077 100) (030 050 068) (052 065 076) (036 042 050) (050 050 050)

1198654

11986541

11986542

11986543

11986544

11986541

(050 050 050) (032 044 056) (024 048 072) (024 060 096)

11986542

(044 056 068) (050 050 050) (042 054 066) (042 066 090)

11986543

(028 052 076) (034 046 058) (050 050 050) (050 062 074)

11986544

(004 040 076) (010 034 058) (026 038 050) (050 050 050)

1198655

11986551

11986552

11986553

11986554

11986555

11986551

(050 050 050) (063 068 072) (055 065 075) (056 075 091) (056 079 100)

11986552

(028 032 037) (050 050 050) (042 047 053) (044 056 069) (044 061 078)

11986553

(025 035 045) (047 053 058) (050 050 050) (052 059 066) (052 064 075)

11986554

(009 025 044) (031 044 056) (034 041 048) (050 050 050) (050 055 059)

11986555

(000 021 044) (022 039 056) (025 036 048) (041 045 050) (050 050 050)

members of a software development company are the same asthe first group For each dimension the ranking results of theimpact degree for risk factors are somewhat different from thefirst group For example among the first risk dimension (119865

1)

incapable organization management (11986511) is also considered

as the most impacting risk factor in the first group but itis the factor having the second greatest impact for globalaspects which is not the same as the first group The mostdifference in ranking for factors of dimensions between thesetwo groups was for the third risk dimension (119865

3) The second

group considers reliance on a few key personnel (11986531) as the

most important factor in the ldquopersonnel system riskrdquo aspectbut it has the least impact based on the evaluations of the firstgroup

According to the results of this case study whether it istechnology enterprise (demander) or software development

company (supplier) they should realize that organization andcommunicationmanagement is the upmost restrict conditionfor the success of software development project that isorganizational culture organizational structure organiza-tional processes organizationrsquos established communicationschannels and so forth The internal and external enterpriseenvironmental factors will critically influence the perfor-mance of the software development project It indicates thatthe application of appropriate project management skills andknowledge is necessary

5 Conclusions

There is an old saying that goes ldquoAn ounce of preventionis worth a pound of curerdquo Therefore if we can understandthe encountered risks and pay more attention in advance

Mathematical Problems in Engineering 7

Table 8 Aggregation decision matrix of the risk dimensions from the second group

1198651

1198652

1198653

1198654

1198655

1198651

(050 050 050) (047 053 060) (053 066 078) (044 064 084) (048 074 100)

1198652

(040 047 053) (050 050 050) (057 063 068) (048 060 074) (051 070 090)

1198653

(022 034 047) (032 038 043) (050 050 050) (041 048 056) (044 058 072)

1198654

(016 036 056) (026 040 052) (044 052 059) (050 050 050) (053 060 066)

1198655

(000 026 052) (010 030 049) (028 042 056) (034 040 047) (050 050 050)

Table 9 Aggregation decision matrix of the risk factors from the second group

1198651

11986511

11986512

11986513

11986514

11986511

(050 050 050) (058 067 076) (033 053 073) (036 068 100)

11986512

(024 033 042) (050 050 050) (026 036 047) (029 052 074)

11986513

(027 047 067) (053 064 074) (050 050 050) (053 065 077)

11986514

(000 032 064) (026 048 071) (023 035 047) (050 050 050)

1198652

11986521

11986522

11986523

11986524

11986521

(050 050 050) (041 052 061) (043 067 089) (000 033 069)

11986522

(039 048 059) (050 050 050) (052 065 078) (009 031 057)

11986523

(011 033 057) (022 035 048) (050 050 050) (007 017 030)

11986524

(031 067 100) (043 069 091) (070 083 093) (050 050 050)

1198653

11986531

11986532

11986533

11986534

11986535

11986531

(050 050 050) (056 063 069) (058 073 085) (043 063 082) (045 074 100)

11986532

(031 037 044) (050 050 050) (052 060 065) (037 050 063) (039 061 081)

11986533

(015 027 042) (035 040 048) (050 050 050) (035 040 048) (037 051 065)

11986534

(018 037 057) (037 050 063) (052 060 065) (050 050 050) (052 061 068)

11986535

(000 026 055) (019 039 061) (035 049 063) (032 039 048) (050 050 050)

1198654

11986541

11986542

11986543

11986544

11986541

(050 050 050) (042 049 056) (045 062 079) (047 073 100)

11986542

(044 051 058) (050 050 050) (053 063 073) (055 074 094)

11986543

(021 038 055) (027 037 047) (050 050 050) (053 062 071)

11986544

(000 027 053) (006 026 045) (029 038 047) (050 050 050)

1198655

11986551

11986552

11986553

11986554

11986555

11986551

(050 050 050) (064 070 074) (059 071 082) (061 082 100) (042 070 097)

11986552

(026 030 036) (050 050 050) (045 051 057) (047 061 076) (028 050 072)

11986553

(018 029 041) (043 049 055) (050 050 050) (052 060 068) (033 049 065)

11986554

(000 018 039) (024 039 053) (032 040 048) (050 050 050) (031 039 047)

11986555

(003 030 058) (028 050 072) (035 051 067) (053 061 069) (050 050 050)

it probably can mitigate loss for the results In this studywe adopt the five risk dimensions and associated twenty-two risk factors were developed by [4] This can help theproject managers to have an overview of the global pictureof risk Then we apply the Fuzzy LinPreRa method whichcan simplify the Fuzzy AHP method and also avoid thenecessity of checking the consistency in the decision-makingprocess to assess project risk for software developmentBecause in the Fuzzy AHP if there are 119899 criteriaattributesit needs 119899(119899 minus 1)2 pairwise comparisons but the FuzzyLinPreRa just requires 119899 minus 1 comparisons and maintainsthe decision matrices consistency The advantage of applyingFuzzy LinPreRa approach compared with Fuzzy AHP isthat the information demand has been significantly reduced

especially in obtaining information from practitioners Thatis it is more convenient to acquire the judgments of practi-tioners or experts of software development industry througha questionnaire

The evaluation results of the experts in both groupsimplied that the impact degrees of the risk dimensions arethe same whatever the rule on the software developmentproject Although there are some differences in the rankingof risk factors for each risk dimension the results shouldprove to be a valuable reference for software developersAccording to the results of the model built it can be seenthat the proposed model can benefit the stakeholders ofsoftware development projects and help them recognize whatrisk factors they may encounter and to facilitate drawing

8 Mathematical Problems in Engineering

Table 10 Impact degree and ranking of risk dimensions and factors for the two groups

Dimensionsfactors Impact degree of the first group Ranking Impact degree of the second group RankingF1 02481 1 02459 1

F11 03246 1 02968 1F12 01829 4 02134 3F13 02793 2 02784 2F14 02133 3 02114 4

F2 02286 2 02306 2F21 03301 1 02537 2F22 02049 3 02432 3F23 01737 4 01731 4F24 02912 2 03300 1

F3 01749 4 01813 4F31 01261 5 02559 1F32 02266 2 02045 2F33 01688 4 01684 4F34 02520 1 02045 3F35 02265 3 01667 5

F4 01813 3 01894 3F41 02553 3 02930 1F42 02777 1 02945 2F43 02589 2 02325 3F44 02082 4 01800 4

F5 01671 5 01528 5F51 02673 1 02716 1F52 01972 3 01934 3F53 02074 2 01888 4F54 01724 4 01500 5F55 01557 5 01962 2

up project risk management strategies for the adequate allo-cation of resources

References

[1] H M Lee ldquoApplying fuzzy set theory to evaluate the rateof aggregative risk in software developmentrdquo Fuzzy Sets andSystems vol 79 no 3 pp 323ndash336 1996

[2] Y H Kwak and J Stoddard ldquoProject risk management lessonslearned from software development environmentrdquo Technova-tion vol 24 no 11 pp 915ndash920 2004

[3] M de Oliveira Barros C M L Werner and G H TravassosldquoSupporting risks in software project managementrdquoThe Journalof Systems and Software vol 70 no 1-2 pp 21ndash35 2004

[4] S T Lu and SHYu ldquoRisk factors assessment for software devel-opment project based on fuzzy decision makingrdquo InternationalJournal of Information and Electronics Engineering vol 2 no 4pp 596ndash600 2012

[5] T-C Wang and Y-H Chen ldquoApplying fuzzy linguistic prefer-ence relations to the improvement of consistency of fuzzy AHPrdquoInformation Sciences vol 178 no 19 pp 3755ndash3765 2008

[6] E Herrera-Viedma F Herrera F Chiclana and M LuqueldquoSome issues on consistency of fuzzy preference relationsrdquoEuropean Journal of Operational Research vol 154 no 1 pp 98ndash109 2004

[7] B W Boehm ldquoSoftware risk management principles andpracticesrdquo IEEE Software vol 8 no 1 pp 32ndash41 1991

[8] H M Lee and L Lin ldquoFuzzy risk presumptive evaluationin software developmentrdquo International Journal of InnovativeComputing Information and Control vol 7 no 7 pp 3881ndash38892011

[9] J Jiang and G Klein ldquoSoftware development risks to projecteffectivenessrdquo The Journal of Systems and Software vol 52 no1 pp 3ndash10 2000

[10] D X Houston G T Mackulak and J S Collofello ldquoStochasticsimulation of risk factor potential effects for software develop-ment risk managementrdquo The Journal of Systems and Softwarevol 59 no 3 pp 247ndash257 2001

[11] G Buyukozkan and D Ruan ldquoChoquet integral based aggre-gation approach to software development risk assessmentrdquoInformation Sciences vol 180 no 3 pp 441ndash451 2010

[12] X N Lu and Q G Ma ldquoRisk analysis in software developmentproject with owners and contractorsrdquo in Proceedings of the IEEEInternational Engineering Management Conference Innovationand Entrepreneurship for Sustainable Development (IEMC rsquo04)vol 2 pp 789ndash793 October 2004

[13] T L Saaty The Analytic Hierarchy Process McGraw-Hill NewYork NY USA 1980

[14] J J Buckley ldquoRanking alternatives using fuzzy numbersrdquo FuzzySets and Systems vol 15 no 1 pp 21ndash31 1985

Mathematical Problems in Engineering 9

[15] S-J Chen and C-L Hwang Fuzzy Multiple Attribute DecisionMaking-Method and Applications Springer New York NYUSA 1992

[16] T L Saaty and L G Vargas The Logic of Priorities KluwerAcademic Boston Mass USA 1982

[17] T Y Hsieh S T Lu and G H Tzeng ldquoFuzzy MCDM approachfor planning and design tenders selection in public officebuildingsrdquo International Journal of Project Management vol 22no 7 pp 573ndash584 2004

[18] S T Lu ldquoUsing the fuzzy multiple criteria decision makingapproach for risk evaluation on investment of overseas projectrdquoin Proceedings of the 9th International Conference on MachineLearning and Cybernetics (ICMLC rsquo10) vol 4 pp 2031ndash2036July 2010

Submit your manuscripts athttpwwwhindawicom

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Mathematical Problems in Engineering

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Function Spaces

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Stochastic AnalysisInternational Journal of

2 Mathematical Problems in Engineering

were identified by Boehm [7] which include personnelshortfalls unrealistic schedules and budgets developingthe wrong functions and properties developing the wronguser interface adding more functionalityfeatures continualrequirement changes shortfalls in externally furnished com-ponents shortfalls in externally performed tasks real-timeperformance shortfalls and straining of computer-sciencecapabilities A hierarchical structure model for evaluatingsoftware development risk was constructed via fuzzy settheory by Lee and Lin [8] They proposed six risk attributesin order to evaluate the aggregative risk personnel systemrequirements schedules and budgets developing technologyexternal resource and performance The fourteen risk itemscan be categorized into six attributes

The twelve risk categories identified by Jiang andKlein [9]include technological acquisition project size lack of generalteam expertise lack of teamrsquos expertise with the task lack ofteamrsquos development expertise lack of user support intensityof conflicts extent of changes brought resources insufficientlack of clarity of role definitions application complexityand lack of user experience In addition Houston et al[10] listed thirty software development risk factors andfurther studied the effects of six common and significant riskfactors They are creeping user requirements lack of staffcommitment lowmorale instability and lack of continuity inproject staffing inaccurate cost estimation excessive sched-ule pressure and lack of senior management commitmentBuyukozkan and Ruan [11] applied the Choquet integralaggregation approach to analyze the effects of importanceand interactions among software development risks Theyextracted software development risk factors by surveying alarge amount of literature and they explored several typesof risks including product engineering risks developmentenvironment risks and program constraint-related risks suchas the main risk dimensions Factors associated with productengineering risks include requirements design code and unittests integration and testing engineering specialists Fac-tors in development environment risks include developmentprocess development system management process manage-ment methods and work environment Resource contractand program interfaces are those factors that influence theprogram constraint risks Lu and Ma [12] identified the riskfactors according to the life cycle of a software developmentproject for owners and contractors For owners the causes ofrisk are distinguished into conceive stage development stageexecution stage and finish stage In the conceive stage anddevelopment stage there are eight risk factors respectivelySix risk factors belong to execution stage but in finish stagethe main risk factor is that there is no standard and criterionof the information system For contractors risk factorsin software development include four aspects policy risktechnique risk scope change risk and management risk Themanagement risk consists of cost management risk qualitymanagement risk schedule management risk integrationmanagement risk human resources management risk andcommunicationmanagement risk Lu and Yu [4] constructeda hierarchical structure of five dimensions and associatedtwenty-two risk factors for software development project and

presented two approaches to assess the importance and theranking of these risk factors by fuzzy set theory The five riskdimensions include organization function risk developingtechnology risk personnel system risk resources integrationrisk and system requirement risk

From these literatures review the software developmentrisk factors were further screened and synthesized for thisstudy We can adopt the hierarchical structure of risk factorsdeveloped by [4] for applying the proposed Fuzzy LinPreRaapproach conveniently Figure 1 shows the hierarchical struc-ture of risk factors for a software development project

3 Method for Assessing the Degree ofImpact of Risk Factors

This study not only would like to realize the risk factors inthe process of software development but is also considerswhich of these factors are important for the projectmanagersIt is impractical to assume that the different project riskfactors equally affect project success Therefore the impactdegree of the risk factors on project success should becarefully evaluated for bettermanaging of the project risk andincreasing the chance of project success That is the varyingeffects of project risk factors on project success provide valu-able information needed to allocate software developmentproject resources This study would like to assess the relativeimpact degree among software development risk factorsfor helping developers to draw up the risk managementstrategies However the largest possible number of evaluationcriteria of a dimension is five If we apply the conventionalanalytic hierarchical process (AHP) proposed by Saaty [13]or fuzzy AHP proposed by Buckley [14] to design the ques-tionnaire we may encounter great difficulties and challengesin collecting information In addition the model also needsto consider the fuzziness of the judgments or opinions ofselected experts when they answer the questionnaires Thusthis study applies the fuzzy linguistic preference relation(Fuzzy LinPreRa) approach for constructing the decisionmatrices of pairwise comparisons The FLPR approach wasconstructed by Wang and Chen [5] based on the consistentfuzzy preference relations (CFPRs) proposed by Herrera-Viedma et al [6] The Fuzzy LinPreRa not only makes it easyfor interviewers to use linguistic variables to present a setof criteria with the least amount of subjective judgment butit also avoids the necessity to check for consistency in thedecision-making process More importantly it is more con-venient to acquire the judgments of practitioners or expertsof software development industry through a questionnaire Abrief introduction of the definitions and steps in the adoptedFuzzy LinPreRa method is given

31 Consistent Fuzzy Preference Relations (CFPRs) The fuzzypreference relation 119875 on a set of evaluation criteria 119883 isa fuzzy set of the product 119883 times 119883 with a membershipfunction 119875 119883 times 119883 rarr [0 1] The preference relation isrepresented by the 119899 times 119899 matrix P = [119901

119894119895] where 119901

119894119895=

119875(119909119894 119909119895) for all 119894 119895 isin 1 119899 Herein 119901

119894119895is interpreted as

the degree of importance of criteria 119909119894over 119909

119895 If 119901119894119895= 05 it

Mathematical Problems in Engineering 3

Softw

are d

evelo

pmen

t risk

organization function risk

developing technology risk

personnel system risk

resources integration risk

system requirement risk

continuing stream of requirements changeslarge number of complex user interfacesdeveloping the wrong software functionadding more functionalityfeatures

lack of contact personrsquos competencein coordination with related divisionslack of quantitative historical datashortfalls in externally furnished components

reliance on a few key personnelunavailability of key staff or project managerlack of staff experience and technologylack of staff commitment and low morale

inexperience with the user environmentoperation

immature developing technologylow productivity in developing technologystraining software and hardwareinadequate scheduling and cost estimation

incapable organization managementinadequate scale of organization

lack of organizational maturity

instability and lack of continuity in project staffing

lack of communication channel in organization

F1

F2

F3

F4

F5

F11F12F13F14

F21F22F23F24

F31F32F33F34F35

F41F42F43F44

F51F52F53F54F55

Figure 1 Hierarchical structure of risk factors for a software development project [4]

means that 119909119894and 119909

119895are equally important119901

119894119895= 1 indicates

that 119909119894is absolutely important to 119909

119895 and 119901

119894119895gt 05 shows

that 119909119894ismore important than 119909

119895 In this case the preference

matrix P is usually assumed to be additive reciprocal thatis 119901119894119895+ 119901119895119894= 1 for all 119894 119895 isin 1 119899 When the reciprocal

fuzzy preference relation P = [119901119894119895] is consistent and verifies

additive consistency there exists a relationship equation suchthat [6]

119901119894(119894+1)

+ 119901(119894+1)(119894+2)

+ sdot sdot sdot + 119901(119895minus1)119895

+ 119901119895119894=(119895 minus 119894 + 1)

2

forall119894 lt 119895

(1)

Equation (1) is very important because it can be usedto construct a consistent fuzzy preference relation from theset of 119899 minus 1 values 119901

12 11990123 119901

(119899minus1)119899 If a decision matrix

with entries in the interval [minus119886 1 + 119886] 119886 gt 0 is outsidethe interval [0 1] it can be constructed by transforming theobtained values using a transformation function that pre-serves reciprocity and additive consistencyThe transformingfunction is 119891 [minus119886 1 + 119886] rarr [0 1] 119891(119909) = (119909 + 119886)(1 + 2119886)In such a way we can facilitate the expression by the evaluatorof consistent preferences in the decision process

32 Linguistic Variables and Fuzzy Numbers A linguisticvariable is the one whose values are words or sentences

expressed in a natural or artificial language Here we usethis kind of expression to compare the impact degree oftwo risk dimensions or factors for a software developmentproject using linguistic terms ldquoabsolutely (not) importantrdquoldquovery strongly (not) importantrdquo ldquoessentially (not) importantrdquoldquoweakly (not) importantrdquo ldquoequally importantrdquo with respectto a triangle fuzzy number (TFN) proposed by [15] A TFNis a fuzzy number on R if its membership function 120583

(119909)

R rarr [0 1] is equal to (2) following the definition in [14]

120583(119909) =

(119909 minus 119897)

(119898 minus 119897) 119897 le 119909 le 119898

(119906 minus 119909)

(119906 minus 119898) 119898 le 119909 le 119906

0 otherwise

(2)

where 119897 and 119906 stand for the lower and upper bounds of thefuzzy number respectively and 119898 stands for the medianvalue The TFN can be denoted by = (119897 119898 119906) and Table 1shows the corresponding TFN for each linguistic assessmentvariable The table of converting linguistic terms to fuzzynumbers is constructed from [15] Detailed conversion scalescan contain andmatch all the verbal terms given by the evalu-ators and it is very important for the evaluators to be familiarwith the decision problem context

4 Mathematical Problems in Engineering

33 Fuzzy Linguistic Preference Relations (Fuzzy LinPreRa)Given a set of criteria 119883 = 119909

1 119909

119899 is associated with

the fuzzy linguistic preference relations matrix P = [119901119894119895] =

(119901119897

119894119895 119901119898

119894119895 119901119906

119894119895) based on consistent fuzzy preference relations

and fuzzy linguistic assessment variables If the matrix abovecomplies with additive reciprocal consistency then the fol-lowing statements must be equivalent

119901119897

119894119895+ 119901119906

119895119894= 1 forall119894 119895 isin 1 119899

119901119898

119894119895+ 119901119898

119894119895= 1 forall119894 119895 isin 1 119899

119901119906

119894119895+ 119901119897

119894119895= 1 forall119894 119895 isin 1 119899

119901119897

119894119895+ 119901119897

119895119896+ 119901119906

119896119894= 15 forall119894 119895 isin 1 119899

119901119898

119894119895+ 119901119898

119895119896+ 119901119898

119896119894= 15 forall119894 lt 119895 lt 119896

119901119906

119894119895+ 119901119906

119895119896+ 119901119897

119896119894= 15 forall119894 lt 119895 lt 119896

119901119897

119894(119894+1)+ 119901119897

(119894+1)(119894+2)+ sdot sdot sdot + 119901

119897

(119895minus1)119895+ 119901119906

119895119894=(119895 minus 119894 + 1)

2forall119894 lt 119895

119901119898

119894(119894+1)+ 119901119898

(119894+1)(119894+2)+ sdot sdot sdot + 119901

119898

(119895minus1)119895+ 119901119898

119895119894=(119895 minus 119894 + 1)

2forall119894 lt 119895

119901119906

119894(119894+1)+ 119901119906

(119894+1)(119894+2)+ sdot sdot sdot + 119901

119906

(119895minus1)119895+ 119901119897

119895119894=(119895 minus 119894 + 1)

2forall119894 lt 119895

(3)

Notably if the values of the obtained matrix P withelements in the interval [minus119888 1 + 119888] (119888 gt 0) are not in theinterval [0 1] the obtained fuzzy numbers will need to betransformed by way of a transformation function to preservethe reciprocity and additive consistency The transformationfunctions for left median and upper values of TFN in everyelement of decision matrix P are given in (4) Finally we canobtain a consistent additive reciprocal decision matrix P1015840

119891 (119909119897) =

(119909119897+ 119888)

(1 + 2119888)

119891 (119909119898) =

(119909119898+ 119888)

(1 + 2119888)

119891 (119909119906) =

(119909119906minus 119888)

(1 + 2119888)

(4)

34 Determination of Criteria Weights If there are 119898 eval-uators to participate in the judgments this study uses thenotion of the average value to integrate the fuzzy judg-ment values of 119898 evaluators from the set of 119899 minus 1 val-ues 119901

12 11990123 119901

(119899minus1)119899 that is

119901119894119895= (

1

119898) otimes (119901

1

119894119895oplus 1199012

119894119895oplus sdot sdot sdot oplus 119901

119898

119894119895) (5)

Here we can establish an original synthetic fuzzy judg-ment matrix P and then use (3) and (4) to obtain the con-sistent synthetic fuzzy judgment matrix P1015840 In order to obtain

Table 1 Fuzzy linguistic assessment variables

Linguistic variables Triangle fuzzy numbersAbsolutely important (AB) (090 100 100)Very strongly important (VS) (080 090 100)Essentially important (ES) (050 070 090)Weakly important (WK) (050 060 070)Equally important (EQ) (040 050 060)Weakly not important (WN) (030 040 050)Essentially not important (EN) (010 030 050)Very strongly not important (VN) (000 010 020)Absolutely not important (AN) (000 000 010)

Table 2 Original evaluation results for the risk dimensions by thefirst group

E1 E2 E3 E4 E5

F1 VS VS EQ WN VN F2

F2 VN VS EQ AB AB F3

F3 VS VN WN VS VN F4

F4 EQ EN VS WK EQ F5

the weights of each criterion this study adopts column vectoraverage approach proposed by Saaty and Vargas [16] asfollows

119903119894119895=

119901119894119895

1199011119895oplus 1199012119895oplus sdot sdot sdot oplus 119901

119899119895

119908119894=1

119899(1199031198941oplus 1199031198942oplus sdot sdot sdot oplus 119903

119894119899) = (119908

119897

119894 119908119898

119894 119908119906

119894)

(6)

The result of the fuzzy synthetic decision reached byeach criterion is a fuzzy number (119908119897

119894 119908119898

119894 119908119906

119894) Therefore it

is necessary that a defuzzification method for fuzzy numbersis used Methods for such defuzzified weighting generallyinclude the mean of maximal (MOM) center of area (COA)and 120572-cut methods [17 18] This study utilizes the COAmethod to find that the nonfuzzy value is a simple and practi-cal methodThe defuzzified weights of the fuzzy number canbe found by the following equation

119908119894=

(119908119897

119894+ 119908119898

119894+ 119908119906

119894)

3forall119894 (7)

4 Case Study

Two companies were invited to answer the questionnairerelated to the risk of a software development project Thefirst group is comprised of five experts with 5 to 15 yearsrsquoexperience in the information management division from amedium scale technology enterpriseThe second group is alsocomprised of five experts with 5 to 10 yearsrsquo experience inestablishing enterprise resource planning (ERP) systems fora software development company The individuals in the twogroups were invited to provide responses to the questionnaire

Mathematical Problems in Engineering 5

Table 3 Original evaluation results for the risk dimensions by thesecond group

E1 E2 E3 E4 E5

F1 ES VS VN WK EQ F2

F2 EQ WN VS VS VS F3

F3 ES VS EN AN WN F4

F4 ES WK EQ AB WK F5

Table 4 Original evaluation results for the risk factors by the firstgroup

E1 E2 E3 E4 E5

1198651

F11 VS AB VS EQ AB F12

F12 VN VN VN ES EN F13

F 13 AB WK EQ ES WK F14

1198652

11986521

VS AB VS WK ES F22

11986522

VS EQ WK WK EN F23

11986523

AN VN EN EQ VN F24

1198653

F31 AN VN EQ VN AN F32

F32 VS VS WK VN AB F33

F33 AN AN VN AN VS F34

F34 EQ VS AB EQ VN F35

1198654

F41 EQ EN EQ WN EQ F42

F42 VS VN VN ES VS F43

F43 EQ ES WK VS WN F44

1198655

F51 VS AB AB VS ES F52

F52 EQ VS WN VN EN F53

F53 EQ VS ES ES ES F54

F54 VS VN WK VS EQ F55

survey and were asked to compare the relative degree ofimpact for the risk dimensions and factors identified inthis study in pairwise sequential order That is they onlyneeded to compare the relative impact degree from 119865

1to

1198652 from 119865

2to 1198653 from 119865

3to 1198654 from 119865

4to 1198655 from 119865

11

to 11986512 from 119865

12to 11986513 and so on Tables 2 and 3 list the

original evaluation results of this pairwise comparison for therisk dimensions given by the five experts of the two groupsSimilarly Tables 4 and 5 display the original pairwise compar-ison matrix for the twenty-two risk factors given by the twogroups Since the preferences and experiences of these expertsare different we use the fuzzy linguistic assessment variablesas in Table 1 and from (3) to (5) to aggregate the expertsrsquosubjective judgments toward the impact of the degree of riskdimensions and factors yielding the synthesized triangularfuzzy numbers listed in Tables 6 7 8 and 9 respectively Theranking of the impact degree is determined by constructinga crisp value from the fuzzy number Hence defuzzificationneeds to be performed to arrange the fuzzy numbers for

Table 5Original evaluation results for the risk factors by the secondgroup

E1 E2 E3 E4 E5

1198651

F11 VS ES EQ VS WK F12

F12 WN EN EQ VN EN F13

F13 ES ES EQ VS ES F14

1198652

F21 WN EN EQ AB WN F22

F22 ES ES VS VS VN F23

F23 EN VN AN AN EN F24

1198653

11986531

ES VS VN AB VS F32

11986532

ES WK VS AB VN F33

11986533

WN EN EQ AN EQ F34

11986534

ES ES EQ AB EQ F35

1198654

F41 WK ES EQ AN WK F42

F42 ES ES ES VS EQ F43

F43 ES ES EQ VS WK F44

1198655

F51 VS VS AB AB ES F52

F52 EQ EN EQ VS WN F53

F53 EQ ES EQ VS ES F54

F54 EN EN VN EN WN F55

ranking Table 10 lists the impact degree and ranking of riskdimensions and factors for software development projectsobtained by using (6) and (7)

For experts in the first group who are staff members of atechnology enterprise among the identified five dimensionsldquoorganization function riskrdquo was found to be the mostimportant risk dimension to influence software developmentperformance and success ldquoDeveloping technology riskrdquo andldquoresources integration riskrdquo are respectively the second andthird highest impact dimensions affecting software devel-opment project performance ldquoPersonnel system riskrdquo andldquosystem requirement riskrdquo are the last two dimensions insequence in relative importance affecting performance andsuccess of the software development project

For each dimension among the first risk dimensions (1198651)

incapable organizationmanagement (11986511) was considered the

most impact risk factor and it is also the most importantfactor for the global aspect Among the second fourth andfifth dimensions (ie 119865

2 1198654 and 119865

5) immature technology

development (11986521) improper coordination with related divi-

sions (11986542) and continuing stream of requirements changes

(11986551) were all found to be the highest impact risk fac-

tors influencing the software development project successUnavailability of key staff or project managers (119865

32) and

lack of staff commitment and low morale (11986534) respectively

are the most observed prominent risk factors which harmsoftware development project success in each dimension

The points of view in relation to the risk dimensionsexpressed by the experts of the second group who are staff

6 Mathematical Problems in Engineering

Table 6 Aggregation decision matrix of the risk dimensions form the first group

1198651

1198652

1198653

1198654

1198655

1198651

(050 050 050) (047 054 062) (054 069 081) (046 068 087) (041 072 100)

1198652

(038 046 053) (050 050 050) (057 065 069) (049 063 075) (044 068 088)

1198653

(019 031 046) (031 035 043) (050 050 050) (041 049 056) (037 053 069)

1198654

(013 032 054) (025 037 051) (044 051 059) (050 050 050) (046 054 063)

1198655

(000 028 059) (012 032 056) (031 047 063) (037 046 054) (050 050 050)

Table 7 Aggregation decision matrix of the risk factors from the first group

1198651

11986511

11986512

11986513

11986514

11986511

(050 050 050) (072 080 085) (040 060 077) (045 075 100)

11986512

(015 020 028) (050 050 050) (018 030 042) (023 045 065)

11986513

(023 040 060) (058 070 082) (050 050 050) (055 065 073)

11986514

(000 025 055) (035 055 077) (027 035 045) (050 050 050)

1198652

11986521

11986522

11986523

11986524

11986521

(050 050 050) (066 076 084) (063 082 100) (031 058 085)

11986522

(016 024 034) (050 050 050) (047 056 066) (015 032 052)

11986523

(000 018 037) (034 044 053) (050 050 050) (018 026 035)

11986524

(015 042 069) (048 068 085) (065 074 082) (050 050 050)

1198653

11986531

11986532

11986533

11986534

11986535

11986531

(050 050 050) (018 023 030) (026 038 052) (000 015 036) (000 023 050)

11986532

(070 077 082) (050 050 050) (058 065 071) (032 042 056) (032 050 070)

11986533

(048 062 074) (029 035 042) (050 050 050) (024 027 035) (024 035 048)

11986534

(064 085 100) (044 058 068) (065 073 076) (050 050 050) (050 058 064)

11986535

(050 077 100) (030 050 068) (052 065 076) (036 042 050) (050 050 050)

1198654

11986541

11986542

11986543

11986544

11986541

(050 050 050) (032 044 056) (024 048 072) (024 060 096)

11986542

(044 056 068) (050 050 050) (042 054 066) (042 066 090)

11986543

(028 052 076) (034 046 058) (050 050 050) (050 062 074)

11986544

(004 040 076) (010 034 058) (026 038 050) (050 050 050)

1198655

11986551

11986552

11986553

11986554

11986555

11986551

(050 050 050) (063 068 072) (055 065 075) (056 075 091) (056 079 100)

11986552

(028 032 037) (050 050 050) (042 047 053) (044 056 069) (044 061 078)

11986553

(025 035 045) (047 053 058) (050 050 050) (052 059 066) (052 064 075)

11986554

(009 025 044) (031 044 056) (034 041 048) (050 050 050) (050 055 059)

11986555

(000 021 044) (022 039 056) (025 036 048) (041 045 050) (050 050 050)

members of a software development company are the same asthe first group For each dimension the ranking results of theimpact degree for risk factors are somewhat different from thefirst group For example among the first risk dimension (119865

1)

incapable organization management (11986511) is also considered

as the most impacting risk factor in the first group but itis the factor having the second greatest impact for globalaspects which is not the same as the first group The mostdifference in ranking for factors of dimensions between thesetwo groups was for the third risk dimension (119865

3) The second

group considers reliance on a few key personnel (11986531) as the

most important factor in the ldquopersonnel system riskrdquo aspectbut it has the least impact based on the evaluations of the firstgroup

According to the results of this case study whether it istechnology enterprise (demander) or software development

company (supplier) they should realize that organization andcommunicationmanagement is the upmost restrict conditionfor the success of software development project that isorganizational culture organizational structure organiza-tional processes organizationrsquos established communicationschannels and so forth The internal and external enterpriseenvironmental factors will critically influence the perfor-mance of the software development project It indicates thatthe application of appropriate project management skills andknowledge is necessary

5 Conclusions

There is an old saying that goes ldquoAn ounce of preventionis worth a pound of curerdquo Therefore if we can understandthe encountered risks and pay more attention in advance

Mathematical Problems in Engineering 7

Table 8 Aggregation decision matrix of the risk dimensions from the second group

1198651

1198652

1198653

1198654

1198655

1198651

(050 050 050) (047 053 060) (053 066 078) (044 064 084) (048 074 100)

1198652

(040 047 053) (050 050 050) (057 063 068) (048 060 074) (051 070 090)

1198653

(022 034 047) (032 038 043) (050 050 050) (041 048 056) (044 058 072)

1198654

(016 036 056) (026 040 052) (044 052 059) (050 050 050) (053 060 066)

1198655

(000 026 052) (010 030 049) (028 042 056) (034 040 047) (050 050 050)

Table 9 Aggregation decision matrix of the risk factors from the second group

1198651

11986511

11986512

11986513

11986514

11986511

(050 050 050) (058 067 076) (033 053 073) (036 068 100)

11986512

(024 033 042) (050 050 050) (026 036 047) (029 052 074)

11986513

(027 047 067) (053 064 074) (050 050 050) (053 065 077)

11986514

(000 032 064) (026 048 071) (023 035 047) (050 050 050)

1198652

11986521

11986522

11986523

11986524

11986521

(050 050 050) (041 052 061) (043 067 089) (000 033 069)

11986522

(039 048 059) (050 050 050) (052 065 078) (009 031 057)

11986523

(011 033 057) (022 035 048) (050 050 050) (007 017 030)

11986524

(031 067 100) (043 069 091) (070 083 093) (050 050 050)

1198653

11986531

11986532

11986533

11986534

11986535

11986531

(050 050 050) (056 063 069) (058 073 085) (043 063 082) (045 074 100)

11986532

(031 037 044) (050 050 050) (052 060 065) (037 050 063) (039 061 081)

11986533

(015 027 042) (035 040 048) (050 050 050) (035 040 048) (037 051 065)

11986534

(018 037 057) (037 050 063) (052 060 065) (050 050 050) (052 061 068)

11986535

(000 026 055) (019 039 061) (035 049 063) (032 039 048) (050 050 050)

1198654

11986541

11986542

11986543

11986544

11986541

(050 050 050) (042 049 056) (045 062 079) (047 073 100)

11986542

(044 051 058) (050 050 050) (053 063 073) (055 074 094)

11986543

(021 038 055) (027 037 047) (050 050 050) (053 062 071)

11986544

(000 027 053) (006 026 045) (029 038 047) (050 050 050)

1198655

11986551

11986552

11986553

11986554

11986555

11986551

(050 050 050) (064 070 074) (059 071 082) (061 082 100) (042 070 097)

11986552

(026 030 036) (050 050 050) (045 051 057) (047 061 076) (028 050 072)

11986553

(018 029 041) (043 049 055) (050 050 050) (052 060 068) (033 049 065)

11986554

(000 018 039) (024 039 053) (032 040 048) (050 050 050) (031 039 047)

11986555

(003 030 058) (028 050 072) (035 051 067) (053 061 069) (050 050 050)

it probably can mitigate loss for the results In this studywe adopt the five risk dimensions and associated twenty-two risk factors were developed by [4] This can help theproject managers to have an overview of the global pictureof risk Then we apply the Fuzzy LinPreRa method whichcan simplify the Fuzzy AHP method and also avoid thenecessity of checking the consistency in the decision-makingprocess to assess project risk for software developmentBecause in the Fuzzy AHP if there are 119899 criteriaattributesit needs 119899(119899 minus 1)2 pairwise comparisons but the FuzzyLinPreRa just requires 119899 minus 1 comparisons and maintainsthe decision matrices consistency The advantage of applyingFuzzy LinPreRa approach compared with Fuzzy AHP isthat the information demand has been significantly reduced

especially in obtaining information from practitioners Thatis it is more convenient to acquire the judgments of practi-tioners or experts of software development industry througha questionnaire

The evaluation results of the experts in both groupsimplied that the impact degrees of the risk dimensions arethe same whatever the rule on the software developmentproject Although there are some differences in the rankingof risk factors for each risk dimension the results shouldprove to be a valuable reference for software developersAccording to the results of the model built it can be seenthat the proposed model can benefit the stakeholders ofsoftware development projects and help them recognize whatrisk factors they may encounter and to facilitate drawing

8 Mathematical Problems in Engineering

Table 10 Impact degree and ranking of risk dimensions and factors for the two groups

Dimensionsfactors Impact degree of the first group Ranking Impact degree of the second group RankingF1 02481 1 02459 1

F11 03246 1 02968 1F12 01829 4 02134 3F13 02793 2 02784 2F14 02133 3 02114 4

F2 02286 2 02306 2F21 03301 1 02537 2F22 02049 3 02432 3F23 01737 4 01731 4F24 02912 2 03300 1

F3 01749 4 01813 4F31 01261 5 02559 1F32 02266 2 02045 2F33 01688 4 01684 4F34 02520 1 02045 3F35 02265 3 01667 5

F4 01813 3 01894 3F41 02553 3 02930 1F42 02777 1 02945 2F43 02589 2 02325 3F44 02082 4 01800 4

F5 01671 5 01528 5F51 02673 1 02716 1F52 01972 3 01934 3F53 02074 2 01888 4F54 01724 4 01500 5F55 01557 5 01962 2

up project risk management strategies for the adequate allo-cation of resources

References

[1] H M Lee ldquoApplying fuzzy set theory to evaluate the rateof aggregative risk in software developmentrdquo Fuzzy Sets andSystems vol 79 no 3 pp 323ndash336 1996

[2] Y H Kwak and J Stoddard ldquoProject risk management lessonslearned from software development environmentrdquo Technova-tion vol 24 no 11 pp 915ndash920 2004

[3] M de Oliveira Barros C M L Werner and G H TravassosldquoSupporting risks in software project managementrdquoThe Journalof Systems and Software vol 70 no 1-2 pp 21ndash35 2004

[4] S T Lu and SHYu ldquoRisk factors assessment for software devel-opment project based on fuzzy decision makingrdquo InternationalJournal of Information and Electronics Engineering vol 2 no 4pp 596ndash600 2012

[5] T-C Wang and Y-H Chen ldquoApplying fuzzy linguistic prefer-ence relations to the improvement of consistency of fuzzy AHPrdquoInformation Sciences vol 178 no 19 pp 3755ndash3765 2008

[6] E Herrera-Viedma F Herrera F Chiclana and M LuqueldquoSome issues on consistency of fuzzy preference relationsrdquoEuropean Journal of Operational Research vol 154 no 1 pp 98ndash109 2004

[7] B W Boehm ldquoSoftware risk management principles andpracticesrdquo IEEE Software vol 8 no 1 pp 32ndash41 1991

[8] H M Lee and L Lin ldquoFuzzy risk presumptive evaluationin software developmentrdquo International Journal of InnovativeComputing Information and Control vol 7 no 7 pp 3881ndash38892011

[9] J Jiang and G Klein ldquoSoftware development risks to projecteffectivenessrdquo The Journal of Systems and Software vol 52 no1 pp 3ndash10 2000

[10] D X Houston G T Mackulak and J S Collofello ldquoStochasticsimulation of risk factor potential effects for software develop-ment risk managementrdquo The Journal of Systems and Softwarevol 59 no 3 pp 247ndash257 2001

[11] G Buyukozkan and D Ruan ldquoChoquet integral based aggre-gation approach to software development risk assessmentrdquoInformation Sciences vol 180 no 3 pp 441ndash451 2010

[12] X N Lu and Q G Ma ldquoRisk analysis in software developmentproject with owners and contractorsrdquo in Proceedings of the IEEEInternational Engineering Management Conference Innovationand Entrepreneurship for Sustainable Development (IEMC rsquo04)vol 2 pp 789ndash793 October 2004

[13] T L Saaty The Analytic Hierarchy Process McGraw-Hill NewYork NY USA 1980

[14] J J Buckley ldquoRanking alternatives using fuzzy numbersrdquo FuzzySets and Systems vol 15 no 1 pp 21ndash31 1985

Mathematical Problems in Engineering 9

[15] S-J Chen and C-L Hwang Fuzzy Multiple Attribute DecisionMaking-Method and Applications Springer New York NYUSA 1992

[16] T L Saaty and L G Vargas The Logic of Priorities KluwerAcademic Boston Mass USA 1982

[17] T Y Hsieh S T Lu and G H Tzeng ldquoFuzzy MCDM approachfor planning and design tenders selection in public officebuildingsrdquo International Journal of Project Management vol 22no 7 pp 573ndash584 2004

[18] S T Lu ldquoUsing the fuzzy multiple criteria decision makingapproach for risk evaluation on investment of overseas projectrdquoin Proceedings of the 9th International Conference on MachineLearning and Cybernetics (ICMLC rsquo10) vol 4 pp 2031ndash2036July 2010

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

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OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Discrete Dynamics in Nature and Society

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Decision SciencesAdvances in

Discrete MathematicsJournal of

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 3

Softw

are d

evelo

pmen

t risk

organization function risk

developing technology risk

personnel system risk

resources integration risk

system requirement risk

continuing stream of requirements changeslarge number of complex user interfacesdeveloping the wrong software functionadding more functionalityfeatures

lack of contact personrsquos competencein coordination with related divisionslack of quantitative historical datashortfalls in externally furnished components

reliance on a few key personnelunavailability of key staff or project managerlack of staff experience and technologylack of staff commitment and low morale

inexperience with the user environmentoperation

immature developing technologylow productivity in developing technologystraining software and hardwareinadequate scheduling and cost estimation

incapable organization managementinadequate scale of organization

lack of organizational maturity

instability and lack of continuity in project staffing

lack of communication channel in organization

F1

F2

F3

F4

F5

F11F12F13F14

F21F22F23F24

F31F32F33F34F35

F41F42F43F44

F51F52F53F54F55

Figure 1 Hierarchical structure of risk factors for a software development project [4]

means that 119909119894and 119909

119895are equally important119901

119894119895= 1 indicates

that 119909119894is absolutely important to 119909

119895 and 119901

119894119895gt 05 shows

that 119909119894ismore important than 119909

119895 In this case the preference

matrix P is usually assumed to be additive reciprocal thatis 119901119894119895+ 119901119895119894= 1 for all 119894 119895 isin 1 119899 When the reciprocal

fuzzy preference relation P = [119901119894119895] is consistent and verifies

additive consistency there exists a relationship equation suchthat [6]

119901119894(119894+1)

+ 119901(119894+1)(119894+2)

+ sdot sdot sdot + 119901(119895minus1)119895

+ 119901119895119894=(119895 minus 119894 + 1)

2

forall119894 lt 119895

(1)

Equation (1) is very important because it can be usedto construct a consistent fuzzy preference relation from theset of 119899 minus 1 values 119901

12 11990123 119901

(119899minus1)119899 If a decision matrix

with entries in the interval [minus119886 1 + 119886] 119886 gt 0 is outsidethe interval [0 1] it can be constructed by transforming theobtained values using a transformation function that pre-serves reciprocity and additive consistencyThe transformingfunction is 119891 [minus119886 1 + 119886] rarr [0 1] 119891(119909) = (119909 + 119886)(1 + 2119886)In such a way we can facilitate the expression by the evaluatorof consistent preferences in the decision process

32 Linguistic Variables and Fuzzy Numbers A linguisticvariable is the one whose values are words or sentences

expressed in a natural or artificial language Here we usethis kind of expression to compare the impact degree oftwo risk dimensions or factors for a software developmentproject using linguistic terms ldquoabsolutely (not) importantrdquoldquovery strongly (not) importantrdquo ldquoessentially (not) importantrdquoldquoweakly (not) importantrdquo ldquoequally importantrdquo with respectto a triangle fuzzy number (TFN) proposed by [15] A TFNis a fuzzy number on R if its membership function 120583

(119909)

R rarr [0 1] is equal to (2) following the definition in [14]

120583(119909) =

(119909 minus 119897)

(119898 minus 119897) 119897 le 119909 le 119898

(119906 minus 119909)

(119906 minus 119898) 119898 le 119909 le 119906

0 otherwise

(2)

where 119897 and 119906 stand for the lower and upper bounds of thefuzzy number respectively and 119898 stands for the medianvalue The TFN can be denoted by = (119897 119898 119906) and Table 1shows the corresponding TFN for each linguistic assessmentvariable The table of converting linguistic terms to fuzzynumbers is constructed from [15] Detailed conversion scalescan contain andmatch all the verbal terms given by the evalu-ators and it is very important for the evaluators to be familiarwith the decision problem context

4 Mathematical Problems in Engineering

33 Fuzzy Linguistic Preference Relations (Fuzzy LinPreRa)Given a set of criteria 119883 = 119909

1 119909

119899 is associated with

the fuzzy linguistic preference relations matrix P = [119901119894119895] =

(119901119897

119894119895 119901119898

119894119895 119901119906

119894119895) based on consistent fuzzy preference relations

and fuzzy linguistic assessment variables If the matrix abovecomplies with additive reciprocal consistency then the fol-lowing statements must be equivalent

119901119897

119894119895+ 119901119906

119895119894= 1 forall119894 119895 isin 1 119899

119901119898

119894119895+ 119901119898

119894119895= 1 forall119894 119895 isin 1 119899

119901119906

119894119895+ 119901119897

119894119895= 1 forall119894 119895 isin 1 119899

119901119897

119894119895+ 119901119897

119895119896+ 119901119906

119896119894= 15 forall119894 119895 isin 1 119899

119901119898

119894119895+ 119901119898

119895119896+ 119901119898

119896119894= 15 forall119894 lt 119895 lt 119896

119901119906

119894119895+ 119901119906

119895119896+ 119901119897

119896119894= 15 forall119894 lt 119895 lt 119896

119901119897

119894(119894+1)+ 119901119897

(119894+1)(119894+2)+ sdot sdot sdot + 119901

119897

(119895minus1)119895+ 119901119906

119895119894=(119895 minus 119894 + 1)

2forall119894 lt 119895

119901119898

119894(119894+1)+ 119901119898

(119894+1)(119894+2)+ sdot sdot sdot + 119901

119898

(119895minus1)119895+ 119901119898

119895119894=(119895 minus 119894 + 1)

2forall119894 lt 119895

119901119906

119894(119894+1)+ 119901119906

(119894+1)(119894+2)+ sdot sdot sdot + 119901

119906

(119895minus1)119895+ 119901119897

119895119894=(119895 minus 119894 + 1)

2forall119894 lt 119895

(3)

Notably if the values of the obtained matrix P withelements in the interval [minus119888 1 + 119888] (119888 gt 0) are not in theinterval [0 1] the obtained fuzzy numbers will need to betransformed by way of a transformation function to preservethe reciprocity and additive consistency The transformationfunctions for left median and upper values of TFN in everyelement of decision matrix P are given in (4) Finally we canobtain a consistent additive reciprocal decision matrix P1015840

119891 (119909119897) =

(119909119897+ 119888)

(1 + 2119888)

119891 (119909119898) =

(119909119898+ 119888)

(1 + 2119888)

119891 (119909119906) =

(119909119906minus 119888)

(1 + 2119888)

(4)

34 Determination of Criteria Weights If there are 119898 eval-uators to participate in the judgments this study uses thenotion of the average value to integrate the fuzzy judg-ment values of 119898 evaluators from the set of 119899 minus 1 val-ues 119901

12 11990123 119901

(119899minus1)119899 that is

119901119894119895= (

1

119898) otimes (119901

1

119894119895oplus 1199012

119894119895oplus sdot sdot sdot oplus 119901

119898

119894119895) (5)

Here we can establish an original synthetic fuzzy judg-ment matrix P and then use (3) and (4) to obtain the con-sistent synthetic fuzzy judgment matrix P1015840 In order to obtain

Table 1 Fuzzy linguistic assessment variables

Linguistic variables Triangle fuzzy numbersAbsolutely important (AB) (090 100 100)Very strongly important (VS) (080 090 100)Essentially important (ES) (050 070 090)Weakly important (WK) (050 060 070)Equally important (EQ) (040 050 060)Weakly not important (WN) (030 040 050)Essentially not important (EN) (010 030 050)Very strongly not important (VN) (000 010 020)Absolutely not important (AN) (000 000 010)

Table 2 Original evaluation results for the risk dimensions by thefirst group

E1 E2 E3 E4 E5

F1 VS VS EQ WN VN F2

F2 VN VS EQ AB AB F3

F3 VS VN WN VS VN F4

F4 EQ EN VS WK EQ F5

the weights of each criterion this study adopts column vectoraverage approach proposed by Saaty and Vargas [16] asfollows

119903119894119895=

119901119894119895

1199011119895oplus 1199012119895oplus sdot sdot sdot oplus 119901

119899119895

119908119894=1

119899(1199031198941oplus 1199031198942oplus sdot sdot sdot oplus 119903

119894119899) = (119908

119897

119894 119908119898

119894 119908119906

119894)

(6)

The result of the fuzzy synthetic decision reached byeach criterion is a fuzzy number (119908119897

119894 119908119898

119894 119908119906

119894) Therefore it

is necessary that a defuzzification method for fuzzy numbersis used Methods for such defuzzified weighting generallyinclude the mean of maximal (MOM) center of area (COA)and 120572-cut methods [17 18] This study utilizes the COAmethod to find that the nonfuzzy value is a simple and practi-cal methodThe defuzzified weights of the fuzzy number canbe found by the following equation

119908119894=

(119908119897

119894+ 119908119898

119894+ 119908119906

119894)

3forall119894 (7)

4 Case Study

Two companies were invited to answer the questionnairerelated to the risk of a software development project Thefirst group is comprised of five experts with 5 to 15 yearsrsquoexperience in the information management division from amedium scale technology enterpriseThe second group is alsocomprised of five experts with 5 to 10 yearsrsquo experience inestablishing enterprise resource planning (ERP) systems fora software development company The individuals in the twogroups were invited to provide responses to the questionnaire

Mathematical Problems in Engineering 5

Table 3 Original evaluation results for the risk dimensions by thesecond group

E1 E2 E3 E4 E5

F1 ES VS VN WK EQ F2

F2 EQ WN VS VS VS F3

F3 ES VS EN AN WN F4

F4 ES WK EQ AB WK F5

Table 4 Original evaluation results for the risk factors by the firstgroup

E1 E2 E3 E4 E5

1198651

F11 VS AB VS EQ AB F12

F12 VN VN VN ES EN F13

F 13 AB WK EQ ES WK F14

1198652

11986521

VS AB VS WK ES F22

11986522

VS EQ WK WK EN F23

11986523

AN VN EN EQ VN F24

1198653

F31 AN VN EQ VN AN F32

F32 VS VS WK VN AB F33

F33 AN AN VN AN VS F34

F34 EQ VS AB EQ VN F35

1198654

F41 EQ EN EQ WN EQ F42

F42 VS VN VN ES VS F43

F43 EQ ES WK VS WN F44

1198655

F51 VS AB AB VS ES F52

F52 EQ VS WN VN EN F53

F53 EQ VS ES ES ES F54

F54 VS VN WK VS EQ F55

survey and were asked to compare the relative degree ofimpact for the risk dimensions and factors identified inthis study in pairwise sequential order That is they onlyneeded to compare the relative impact degree from 119865

1to

1198652 from 119865

2to 1198653 from 119865

3to 1198654 from 119865

4to 1198655 from 119865

11

to 11986512 from 119865

12to 11986513 and so on Tables 2 and 3 list the

original evaluation results of this pairwise comparison for therisk dimensions given by the five experts of the two groupsSimilarly Tables 4 and 5 display the original pairwise compar-ison matrix for the twenty-two risk factors given by the twogroups Since the preferences and experiences of these expertsare different we use the fuzzy linguistic assessment variablesas in Table 1 and from (3) to (5) to aggregate the expertsrsquosubjective judgments toward the impact of the degree of riskdimensions and factors yielding the synthesized triangularfuzzy numbers listed in Tables 6 7 8 and 9 respectively Theranking of the impact degree is determined by constructinga crisp value from the fuzzy number Hence defuzzificationneeds to be performed to arrange the fuzzy numbers for

Table 5Original evaluation results for the risk factors by the secondgroup

E1 E2 E3 E4 E5

1198651

F11 VS ES EQ VS WK F12

F12 WN EN EQ VN EN F13

F13 ES ES EQ VS ES F14

1198652

F21 WN EN EQ AB WN F22

F22 ES ES VS VS VN F23

F23 EN VN AN AN EN F24

1198653

11986531

ES VS VN AB VS F32

11986532

ES WK VS AB VN F33

11986533

WN EN EQ AN EQ F34

11986534

ES ES EQ AB EQ F35

1198654

F41 WK ES EQ AN WK F42

F42 ES ES ES VS EQ F43

F43 ES ES EQ VS WK F44

1198655

F51 VS VS AB AB ES F52

F52 EQ EN EQ VS WN F53

F53 EQ ES EQ VS ES F54

F54 EN EN VN EN WN F55

ranking Table 10 lists the impact degree and ranking of riskdimensions and factors for software development projectsobtained by using (6) and (7)

For experts in the first group who are staff members of atechnology enterprise among the identified five dimensionsldquoorganization function riskrdquo was found to be the mostimportant risk dimension to influence software developmentperformance and success ldquoDeveloping technology riskrdquo andldquoresources integration riskrdquo are respectively the second andthird highest impact dimensions affecting software devel-opment project performance ldquoPersonnel system riskrdquo andldquosystem requirement riskrdquo are the last two dimensions insequence in relative importance affecting performance andsuccess of the software development project

For each dimension among the first risk dimensions (1198651)

incapable organizationmanagement (11986511) was considered the

most impact risk factor and it is also the most importantfactor for the global aspect Among the second fourth andfifth dimensions (ie 119865

2 1198654 and 119865

5) immature technology

development (11986521) improper coordination with related divi-

sions (11986542) and continuing stream of requirements changes

(11986551) were all found to be the highest impact risk fac-

tors influencing the software development project successUnavailability of key staff or project managers (119865

32) and

lack of staff commitment and low morale (11986534) respectively

are the most observed prominent risk factors which harmsoftware development project success in each dimension

The points of view in relation to the risk dimensionsexpressed by the experts of the second group who are staff

6 Mathematical Problems in Engineering

Table 6 Aggregation decision matrix of the risk dimensions form the first group

1198651

1198652

1198653

1198654

1198655

1198651

(050 050 050) (047 054 062) (054 069 081) (046 068 087) (041 072 100)

1198652

(038 046 053) (050 050 050) (057 065 069) (049 063 075) (044 068 088)

1198653

(019 031 046) (031 035 043) (050 050 050) (041 049 056) (037 053 069)

1198654

(013 032 054) (025 037 051) (044 051 059) (050 050 050) (046 054 063)

1198655

(000 028 059) (012 032 056) (031 047 063) (037 046 054) (050 050 050)

Table 7 Aggregation decision matrix of the risk factors from the first group

1198651

11986511

11986512

11986513

11986514

11986511

(050 050 050) (072 080 085) (040 060 077) (045 075 100)

11986512

(015 020 028) (050 050 050) (018 030 042) (023 045 065)

11986513

(023 040 060) (058 070 082) (050 050 050) (055 065 073)

11986514

(000 025 055) (035 055 077) (027 035 045) (050 050 050)

1198652

11986521

11986522

11986523

11986524

11986521

(050 050 050) (066 076 084) (063 082 100) (031 058 085)

11986522

(016 024 034) (050 050 050) (047 056 066) (015 032 052)

11986523

(000 018 037) (034 044 053) (050 050 050) (018 026 035)

11986524

(015 042 069) (048 068 085) (065 074 082) (050 050 050)

1198653

11986531

11986532

11986533

11986534

11986535

11986531

(050 050 050) (018 023 030) (026 038 052) (000 015 036) (000 023 050)

11986532

(070 077 082) (050 050 050) (058 065 071) (032 042 056) (032 050 070)

11986533

(048 062 074) (029 035 042) (050 050 050) (024 027 035) (024 035 048)

11986534

(064 085 100) (044 058 068) (065 073 076) (050 050 050) (050 058 064)

11986535

(050 077 100) (030 050 068) (052 065 076) (036 042 050) (050 050 050)

1198654

11986541

11986542

11986543

11986544

11986541

(050 050 050) (032 044 056) (024 048 072) (024 060 096)

11986542

(044 056 068) (050 050 050) (042 054 066) (042 066 090)

11986543

(028 052 076) (034 046 058) (050 050 050) (050 062 074)

11986544

(004 040 076) (010 034 058) (026 038 050) (050 050 050)

1198655

11986551

11986552

11986553

11986554

11986555

11986551

(050 050 050) (063 068 072) (055 065 075) (056 075 091) (056 079 100)

11986552

(028 032 037) (050 050 050) (042 047 053) (044 056 069) (044 061 078)

11986553

(025 035 045) (047 053 058) (050 050 050) (052 059 066) (052 064 075)

11986554

(009 025 044) (031 044 056) (034 041 048) (050 050 050) (050 055 059)

11986555

(000 021 044) (022 039 056) (025 036 048) (041 045 050) (050 050 050)

members of a software development company are the same asthe first group For each dimension the ranking results of theimpact degree for risk factors are somewhat different from thefirst group For example among the first risk dimension (119865

1)

incapable organization management (11986511) is also considered

as the most impacting risk factor in the first group but itis the factor having the second greatest impact for globalaspects which is not the same as the first group The mostdifference in ranking for factors of dimensions between thesetwo groups was for the third risk dimension (119865

3) The second

group considers reliance on a few key personnel (11986531) as the

most important factor in the ldquopersonnel system riskrdquo aspectbut it has the least impact based on the evaluations of the firstgroup

According to the results of this case study whether it istechnology enterprise (demander) or software development

company (supplier) they should realize that organization andcommunicationmanagement is the upmost restrict conditionfor the success of software development project that isorganizational culture organizational structure organiza-tional processes organizationrsquos established communicationschannels and so forth The internal and external enterpriseenvironmental factors will critically influence the perfor-mance of the software development project It indicates thatthe application of appropriate project management skills andknowledge is necessary

5 Conclusions

There is an old saying that goes ldquoAn ounce of preventionis worth a pound of curerdquo Therefore if we can understandthe encountered risks and pay more attention in advance

Mathematical Problems in Engineering 7

Table 8 Aggregation decision matrix of the risk dimensions from the second group

1198651

1198652

1198653

1198654

1198655

1198651

(050 050 050) (047 053 060) (053 066 078) (044 064 084) (048 074 100)

1198652

(040 047 053) (050 050 050) (057 063 068) (048 060 074) (051 070 090)

1198653

(022 034 047) (032 038 043) (050 050 050) (041 048 056) (044 058 072)

1198654

(016 036 056) (026 040 052) (044 052 059) (050 050 050) (053 060 066)

1198655

(000 026 052) (010 030 049) (028 042 056) (034 040 047) (050 050 050)

Table 9 Aggregation decision matrix of the risk factors from the second group

1198651

11986511

11986512

11986513

11986514

11986511

(050 050 050) (058 067 076) (033 053 073) (036 068 100)

11986512

(024 033 042) (050 050 050) (026 036 047) (029 052 074)

11986513

(027 047 067) (053 064 074) (050 050 050) (053 065 077)

11986514

(000 032 064) (026 048 071) (023 035 047) (050 050 050)

1198652

11986521

11986522

11986523

11986524

11986521

(050 050 050) (041 052 061) (043 067 089) (000 033 069)

11986522

(039 048 059) (050 050 050) (052 065 078) (009 031 057)

11986523

(011 033 057) (022 035 048) (050 050 050) (007 017 030)

11986524

(031 067 100) (043 069 091) (070 083 093) (050 050 050)

1198653

11986531

11986532

11986533

11986534

11986535

11986531

(050 050 050) (056 063 069) (058 073 085) (043 063 082) (045 074 100)

11986532

(031 037 044) (050 050 050) (052 060 065) (037 050 063) (039 061 081)

11986533

(015 027 042) (035 040 048) (050 050 050) (035 040 048) (037 051 065)

11986534

(018 037 057) (037 050 063) (052 060 065) (050 050 050) (052 061 068)

11986535

(000 026 055) (019 039 061) (035 049 063) (032 039 048) (050 050 050)

1198654

11986541

11986542

11986543

11986544

11986541

(050 050 050) (042 049 056) (045 062 079) (047 073 100)

11986542

(044 051 058) (050 050 050) (053 063 073) (055 074 094)

11986543

(021 038 055) (027 037 047) (050 050 050) (053 062 071)

11986544

(000 027 053) (006 026 045) (029 038 047) (050 050 050)

1198655

11986551

11986552

11986553

11986554

11986555

11986551

(050 050 050) (064 070 074) (059 071 082) (061 082 100) (042 070 097)

11986552

(026 030 036) (050 050 050) (045 051 057) (047 061 076) (028 050 072)

11986553

(018 029 041) (043 049 055) (050 050 050) (052 060 068) (033 049 065)

11986554

(000 018 039) (024 039 053) (032 040 048) (050 050 050) (031 039 047)

11986555

(003 030 058) (028 050 072) (035 051 067) (053 061 069) (050 050 050)

it probably can mitigate loss for the results In this studywe adopt the five risk dimensions and associated twenty-two risk factors were developed by [4] This can help theproject managers to have an overview of the global pictureof risk Then we apply the Fuzzy LinPreRa method whichcan simplify the Fuzzy AHP method and also avoid thenecessity of checking the consistency in the decision-makingprocess to assess project risk for software developmentBecause in the Fuzzy AHP if there are 119899 criteriaattributesit needs 119899(119899 minus 1)2 pairwise comparisons but the FuzzyLinPreRa just requires 119899 minus 1 comparisons and maintainsthe decision matrices consistency The advantage of applyingFuzzy LinPreRa approach compared with Fuzzy AHP isthat the information demand has been significantly reduced

especially in obtaining information from practitioners Thatis it is more convenient to acquire the judgments of practi-tioners or experts of software development industry througha questionnaire

The evaluation results of the experts in both groupsimplied that the impact degrees of the risk dimensions arethe same whatever the rule on the software developmentproject Although there are some differences in the rankingof risk factors for each risk dimension the results shouldprove to be a valuable reference for software developersAccording to the results of the model built it can be seenthat the proposed model can benefit the stakeholders ofsoftware development projects and help them recognize whatrisk factors they may encounter and to facilitate drawing

8 Mathematical Problems in Engineering

Table 10 Impact degree and ranking of risk dimensions and factors for the two groups

Dimensionsfactors Impact degree of the first group Ranking Impact degree of the second group RankingF1 02481 1 02459 1

F11 03246 1 02968 1F12 01829 4 02134 3F13 02793 2 02784 2F14 02133 3 02114 4

F2 02286 2 02306 2F21 03301 1 02537 2F22 02049 3 02432 3F23 01737 4 01731 4F24 02912 2 03300 1

F3 01749 4 01813 4F31 01261 5 02559 1F32 02266 2 02045 2F33 01688 4 01684 4F34 02520 1 02045 3F35 02265 3 01667 5

F4 01813 3 01894 3F41 02553 3 02930 1F42 02777 1 02945 2F43 02589 2 02325 3F44 02082 4 01800 4

F5 01671 5 01528 5F51 02673 1 02716 1F52 01972 3 01934 3F53 02074 2 01888 4F54 01724 4 01500 5F55 01557 5 01962 2

up project risk management strategies for the adequate allo-cation of resources

References

[1] H M Lee ldquoApplying fuzzy set theory to evaluate the rateof aggregative risk in software developmentrdquo Fuzzy Sets andSystems vol 79 no 3 pp 323ndash336 1996

[2] Y H Kwak and J Stoddard ldquoProject risk management lessonslearned from software development environmentrdquo Technova-tion vol 24 no 11 pp 915ndash920 2004

[3] M de Oliveira Barros C M L Werner and G H TravassosldquoSupporting risks in software project managementrdquoThe Journalof Systems and Software vol 70 no 1-2 pp 21ndash35 2004

[4] S T Lu and SHYu ldquoRisk factors assessment for software devel-opment project based on fuzzy decision makingrdquo InternationalJournal of Information and Electronics Engineering vol 2 no 4pp 596ndash600 2012

[5] T-C Wang and Y-H Chen ldquoApplying fuzzy linguistic prefer-ence relations to the improvement of consistency of fuzzy AHPrdquoInformation Sciences vol 178 no 19 pp 3755ndash3765 2008

[6] E Herrera-Viedma F Herrera F Chiclana and M LuqueldquoSome issues on consistency of fuzzy preference relationsrdquoEuropean Journal of Operational Research vol 154 no 1 pp 98ndash109 2004

[7] B W Boehm ldquoSoftware risk management principles andpracticesrdquo IEEE Software vol 8 no 1 pp 32ndash41 1991

[8] H M Lee and L Lin ldquoFuzzy risk presumptive evaluationin software developmentrdquo International Journal of InnovativeComputing Information and Control vol 7 no 7 pp 3881ndash38892011

[9] J Jiang and G Klein ldquoSoftware development risks to projecteffectivenessrdquo The Journal of Systems and Software vol 52 no1 pp 3ndash10 2000

[10] D X Houston G T Mackulak and J S Collofello ldquoStochasticsimulation of risk factor potential effects for software develop-ment risk managementrdquo The Journal of Systems and Softwarevol 59 no 3 pp 247ndash257 2001

[11] G Buyukozkan and D Ruan ldquoChoquet integral based aggre-gation approach to software development risk assessmentrdquoInformation Sciences vol 180 no 3 pp 441ndash451 2010

[12] X N Lu and Q G Ma ldquoRisk analysis in software developmentproject with owners and contractorsrdquo in Proceedings of the IEEEInternational Engineering Management Conference Innovationand Entrepreneurship for Sustainable Development (IEMC rsquo04)vol 2 pp 789ndash793 October 2004

[13] T L Saaty The Analytic Hierarchy Process McGraw-Hill NewYork NY USA 1980

[14] J J Buckley ldquoRanking alternatives using fuzzy numbersrdquo FuzzySets and Systems vol 15 no 1 pp 21ndash31 1985

Mathematical Problems in Engineering 9

[15] S-J Chen and C-L Hwang Fuzzy Multiple Attribute DecisionMaking-Method and Applications Springer New York NYUSA 1992

[16] T L Saaty and L G Vargas The Logic of Priorities KluwerAcademic Boston Mass USA 1982

[17] T Y Hsieh S T Lu and G H Tzeng ldquoFuzzy MCDM approachfor planning and design tenders selection in public officebuildingsrdquo International Journal of Project Management vol 22no 7 pp 573ndash584 2004

[18] S T Lu ldquoUsing the fuzzy multiple criteria decision makingapproach for risk evaluation on investment of overseas projectrdquoin Proceedings of the 9th International Conference on MachineLearning and Cybernetics (ICMLC rsquo10) vol 4 pp 2031ndash2036July 2010

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

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OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Journal of

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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

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Discrete Dynamics in Nature and Society

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Decision SciencesAdvances in

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

33 Fuzzy Linguistic Preference Relations (Fuzzy LinPreRa)Given a set of criteria 119883 = 119909

1 119909

119899 is associated with

the fuzzy linguistic preference relations matrix P = [119901119894119895] =

(119901119897

119894119895 119901119898

119894119895 119901119906

119894119895) based on consistent fuzzy preference relations

and fuzzy linguistic assessment variables If the matrix abovecomplies with additive reciprocal consistency then the fol-lowing statements must be equivalent

119901119897

119894119895+ 119901119906

119895119894= 1 forall119894 119895 isin 1 119899

119901119898

119894119895+ 119901119898

119894119895= 1 forall119894 119895 isin 1 119899

119901119906

119894119895+ 119901119897

119894119895= 1 forall119894 119895 isin 1 119899

119901119897

119894119895+ 119901119897

119895119896+ 119901119906

119896119894= 15 forall119894 119895 isin 1 119899

119901119898

119894119895+ 119901119898

119895119896+ 119901119898

119896119894= 15 forall119894 lt 119895 lt 119896

119901119906

119894119895+ 119901119906

119895119896+ 119901119897

119896119894= 15 forall119894 lt 119895 lt 119896

119901119897

119894(119894+1)+ 119901119897

(119894+1)(119894+2)+ sdot sdot sdot + 119901

119897

(119895minus1)119895+ 119901119906

119895119894=(119895 minus 119894 + 1)

2forall119894 lt 119895

119901119898

119894(119894+1)+ 119901119898

(119894+1)(119894+2)+ sdot sdot sdot + 119901

119898

(119895minus1)119895+ 119901119898

119895119894=(119895 minus 119894 + 1)

2forall119894 lt 119895

119901119906

119894(119894+1)+ 119901119906

(119894+1)(119894+2)+ sdot sdot sdot + 119901

119906

(119895minus1)119895+ 119901119897

119895119894=(119895 minus 119894 + 1)

2forall119894 lt 119895

(3)

Notably if the values of the obtained matrix P withelements in the interval [minus119888 1 + 119888] (119888 gt 0) are not in theinterval [0 1] the obtained fuzzy numbers will need to betransformed by way of a transformation function to preservethe reciprocity and additive consistency The transformationfunctions for left median and upper values of TFN in everyelement of decision matrix P are given in (4) Finally we canobtain a consistent additive reciprocal decision matrix P1015840

119891 (119909119897) =

(119909119897+ 119888)

(1 + 2119888)

119891 (119909119898) =

(119909119898+ 119888)

(1 + 2119888)

119891 (119909119906) =

(119909119906minus 119888)

(1 + 2119888)

(4)

34 Determination of Criteria Weights If there are 119898 eval-uators to participate in the judgments this study uses thenotion of the average value to integrate the fuzzy judg-ment values of 119898 evaluators from the set of 119899 minus 1 val-ues 119901

12 11990123 119901

(119899minus1)119899 that is

119901119894119895= (

1

119898) otimes (119901

1

119894119895oplus 1199012

119894119895oplus sdot sdot sdot oplus 119901

119898

119894119895) (5)

Here we can establish an original synthetic fuzzy judg-ment matrix P and then use (3) and (4) to obtain the con-sistent synthetic fuzzy judgment matrix P1015840 In order to obtain

Table 1 Fuzzy linguistic assessment variables

Linguistic variables Triangle fuzzy numbersAbsolutely important (AB) (090 100 100)Very strongly important (VS) (080 090 100)Essentially important (ES) (050 070 090)Weakly important (WK) (050 060 070)Equally important (EQ) (040 050 060)Weakly not important (WN) (030 040 050)Essentially not important (EN) (010 030 050)Very strongly not important (VN) (000 010 020)Absolutely not important (AN) (000 000 010)

Table 2 Original evaluation results for the risk dimensions by thefirst group

E1 E2 E3 E4 E5

F1 VS VS EQ WN VN F2

F2 VN VS EQ AB AB F3

F3 VS VN WN VS VN F4

F4 EQ EN VS WK EQ F5

the weights of each criterion this study adopts column vectoraverage approach proposed by Saaty and Vargas [16] asfollows

119903119894119895=

119901119894119895

1199011119895oplus 1199012119895oplus sdot sdot sdot oplus 119901

119899119895

119908119894=1

119899(1199031198941oplus 1199031198942oplus sdot sdot sdot oplus 119903

119894119899) = (119908

119897

119894 119908119898

119894 119908119906

119894)

(6)

The result of the fuzzy synthetic decision reached byeach criterion is a fuzzy number (119908119897

119894 119908119898

119894 119908119906

119894) Therefore it

is necessary that a defuzzification method for fuzzy numbersis used Methods for such defuzzified weighting generallyinclude the mean of maximal (MOM) center of area (COA)and 120572-cut methods [17 18] This study utilizes the COAmethod to find that the nonfuzzy value is a simple and practi-cal methodThe defuzzified weights of the fuzzy number canbe found by the following equation

119908119894=

(119908119897

119894+ 119908119898

119894+ 119908119906

119894)

3forall119894 (7)

4 Case Study

Two companies were invited to answer the questionnairerelated to the risk of a software development project Thefirst group is comprised of five experts with 5 to 15 yearsrsquoexperience in the information management division from amedium scale technology enterpriseThe second group is alsocomprised of five experts with 5 to 10 yearsrsquo experience inestablishing enterprise resource planning (ERP) systems fora software development company The individuals in the twogroups were invited to provide responses to the questionnaire

Mathematical Problems in Engineering 5

Table 3 Original evaluation results for the risk dimensions by thesecond group

E1 E2 E3 E4 E5

F1 ES VS VN WK EQ F2

F2 EQ WN VS VS VS F3

F3 ES VS EN AN WN F4

F4 ES WK EQ AB WK F5

Table 4 Original evaluation results for the risk factors by the firstgroup

E1 E2 E3 E4 E5

1198651

F11 VS AB VS EQ AB F12

F12 VN VN VN ES EN F13

F 13 AB WK EQ ES WK F14

1198652

11986521

VS AB VS WK ES F22

11986522

VS EQ WK WK EN F23

11986523

AN VN EN EQ VN F24

1198653

F31 AN VN EQ VN AN F32

F32 VS VS WK VN AB F33

F33 AN AN VN AN VS F34

F34 EQ VS AB EQ VN F35

1198654

F41 EQ EN EQ WN EQ F42

F42 VS VN VN ES VS F43

F43 EQ ES WK VS WN F44

1198655

F51 VS AB AB VS ES F52

F52 EQ VS WN VN EN F53

F53 EQ VS ES ES ES F54

F54 VS VN WK VS EQ F55

survey and were asked to compare the relative degree ofimpact for the risk dimensions and factors identified inthis study in pairwise sequential order That is they onlyneeded to compare the relative impact degree from 119865

1to

1198652 from 119865

2to 1198653 from 119865

3to 1198654 from 119865

4to 1198655 from 119865

11

to 11986512 from 119865

12to 11986513 and so on Tables 2 and 3 list the

original evaluation results of this pairwise comparison for therisk dimensions given by the five experts of the two groupsSimilarly Tables 4 and 5 display the original pairwise compar-ison matrix for the twenty-two risk factors given by the twogroups Since the preferences and experiences of these expertsare different we use the fuzzy linguistic assessment variablesas in Table 1 and from (3) to (5) to aggregate the expertsrsquosubjective judgments toward the impact of the degree of riskdimensions and factors yielding the synthesized triangularfuzzy numbers listed in Tables 6 7 8 and 9 respectively Theranking of the impact degree is determined by constructinga crisp value from the fuzzy number Hence defuzzificationneeds to be performed to arrange the fuzzy numbers for

Table 5Original evaluation results for the risk factors by the secondgroup

E1 E2 E3 E4 E5

1198651

F11 VS ES EQ VS WK F12

F12 WN EN EQ VN EN F13

F13 ES ES EQ VS ES F14

1198652

F21 WN EN EQ AB WN F22

F22 ES ES VS VS VN F23

F23 EN VN AN AN EN F24

1198653

11986531

ES VS VN AB VS F32

11986532

ES WK VS AB VN F33

11986533

WN EN EQ AN EQ F34

11986534

ES ES EQ AB EQ F35

1198654

F41 WK ES EQ AN WK F42

F42 ES ES ES VS EQ F43

F43 ES ES EQ VS WK F44

1198655

F51 VS VS AB AB ES F52

F52 EQ EN EQ VS WN F53

F53 EQ ES EQ VS ES F54

F54 EN EN VN EN WN F55

ranking Table 10 lists the impact degree and ranking of riskdimensions and factors for software development projectsobtained by using (6) and (7)

For experts in the first group who are staff members of atechnology enterprise among the identified five dimensionsldquoorganization function riskrdquo was found to be the mostimportant risk dimension to influence software developmentperformance and success ldquoDeveloping technology riskrdquo andldquoresources integration riskrdquo are respectively the second andthird highest impact dimensions affecting software devel-opment project performance ldquoPersonnel system riskrdquo andldquosystem requirement riskrdquo are the last two dimensions insequence in relative importance affecting performance andsuccess of the software development project

For each dimension among the first risk dimensions (1198651)

incapable organizationmanagement (11986511) was considered the

most impact risk factor and it is also the most importantfactor for the global aspect Among the second fourth andfifth dimensions (ie 119865

2 1198654 and 119865

5) immature technology

development (11986521) improper coordination with related divi-

sions (11986542) and continuing stream of requirements changes

(11986551) were all found to be the highest impact risk fac-

tors influencing the software development project successUnavailability of key staff or project managers (119865

32) and

lack of staff commitment and low morale (11986534) respectively

are the most observed prominent risk factors which harmsoftware development project success in each dimension

The points of view in relation to the risk dimensionsexpressed by the experts of the second group who are staff

6 Mathematical Problems in Engineering

Table 6 Aggregation decision matrix of the risk dimensions form the first group

1198651

1198652

1198653

1198654

1198655

1198651

(050 050 050) (047 054 062) (054 069 081) (046 068 087) (041 072 100)

1198652

(038 046 053) (050 050 050) (057 065 069) (049 063 075) (044 068 088)

1198653

(019 031 046) (031 035 043) (050 050 050) (041 049 056) (037 053 069)

1198654

(013 032 054) (025 037 051) (044 051 059) (050 050 050) (046 054 063)

1198655

(000 028 059) (012 032 056) (031 047 063) (037 046 054) (050 050 050)

Table 7 Aggregation decision matrix of the risk factors from the first group

1198651

11986511

11986512

11986513

11986514

11986511

(050 050 050) (072 080 085) (040 060 077) (045 075 100)

11986512

(015 020 028) (050 050 050) (018 030 042) (023 045 065)

11986513

(023 040 060) (058 070 082) (050 050 050) (055 065 073)

11986514

(000 025 055) (035 055 077) (027 035 045) (050 050 050)

1198652

11986521

11986522

11986523

11986524

11986521

(050 050 050) (066 076 084) (063 082 100) (031 058 085)

11986522

(016 024 034) (050 050 050) (047 056 066) (015 032 052)

11986523

(000 018 037) (034 044 053) (050 050 050) (018 026 035)

11986524

(015 042 069) (048 068 085) (065 074 082) (050 050 050)

1198653

11986531

11986532

11986533

11986534

11986535

11986531

(050 050 050) (018 023 030) (026 038 052) (000 015 036) (000 023 050)

11986532

(070 077 082) (050 050 050) (058 065 071) (032 042 056) (032 050 070)

11986533

(048 062 074) (029 035 042) (050 050 050) (024 027 035) (024 035 048)

11986534

(064 085 100) (044 058 068) (065 073 076) (050 050 050) (050 058 064)

11986535

(050 077 100) (030 050 068) (052 065 076) (036 042 050) (050 050 050)

1198654

11986541

11986542

11986543

11986544

11986541

(050 050 050) (032 044 056) (024 048 072) (024 060 096)

11986542

(044 056 068) (050 050 050) (042 054 066) (042 066 090)

11986543

(028 052 076) (034 046 058) (050 050 050) (050 062 074)

11986544

(004 040 076) (010 034 058) (026 038 050) (050 050 050)

1198655

11986551

11986552

11986553

11986554

11986555

11986551

(050 050 050) (063 068 072) (055 065 075) (056 075 091) (056 079 100)

11986552

(028 032 037) (050 050 050) (042 047 053) (044 056 069) (044 061 078)

11986553

(025 035 045) (047 053 058) (050 050 050) (052 059 066) (052 064 075)

11986554

(009 025 044) (031 044 056) (034 041 048) (050 050 050) (050 055 059)

11986555

(000 021 044) (022 039 056) (025 036 048) (041 045 050) (050 050 050)

members of a software development company are the same asthe first group For each dimension the ranking results of theimpact degree for risk factors are somewhat different from thefirst group For example among the first risk dimension (119865

1)

incapable organization management (11986511) is also considered

as the most impacting risk factor in the first group but itis the factor having the second greatest impact for globalaspects which is not the same as the first group The mostdifference in ranking for factors of dimensions between thesetwo groups was for the third risk dimension (119865

3) The second

group considers reliance on a few key personnel (11986531) as the

most important factor in the ldquopersonnel system riskrdquo aspectbut it has the least impact based on the evaluations of the firstgroup

According to the results of this case study whether it istechnology enterprise (demander) or software development

company (supplier) they should realize that organization andcommunicationmanagement is the upmost restrict conditionfor the success of software development project that isorganizational culture organizational structure organiza-tional processes organizationrsquos established communicationschannels and so forth The internal and external enterpriseenvironmental factors will critically influence the perfor-mance of the software development project It indicates thatthe application of appropriate project management skills andknowledge is necessary

5 Conclusions

There is an old saying that goes ldquoAn ounce of preventionis worth a pound of curerdquo Therefore if we can understandthe encountered risks and pay more attention in advance

Mathematical Problems in Engineering 7

Table 8 Aggregation decision matrix of the risk dimensions from the second group

1198651

1198652

1198653

1198654

1198655

1198651

(050 050 050) (047 053 060) (053 066 078) (044 064 084) (048 074 100)

1198652

(040 047 053) (050 050 050) (057 063 068) (048 060 074) (051 070 090)

1198653

(022 034 047) (032 038 043) (050 050 050) (041 048 056) (044 058 072)

1198654

(016 036 056) (026 040 052) (044 052 059) (050 050 050) (053 060 066)

1198655

(000 026 052) (010 030 049) (028 042 056) (034 040 047) (050 050 050)

Table 9 Aggregation decision matrix of the risk factors from the second group

1198651

11986511

11986512

11986513

11986514

11986511

(050 050 050) (058 067 076) (033 053 073) (036 068 100)

11986512

(024 033 042) (050 050 050) (026 036 047) (029 052 074)

11986513

(027 047 067) (053 064 074) (050 050 050) (053 065 077)

11986514

(000 032 064) (026 048 071) (023 035 047) (050 050 050)

1198652

11986521

11986522

11986523

11986524

11986521

(050 050 050) (041 052 061) (043 067 089) (000 033 069)

11986522

(039 048 059) (050 050 050) (052 065 078) (009 031 057)

11986523

(011 033 057) (022 035 048) (050 050 050) (007 017 030)

11986524

(031 067 100) (043 069 091) (070 083 093) (050 050 050)

1198653

11986531

11986532

11986533

11986534

11986535

11986531

(050 050 050) (056 063 069) (058 073 085) (043 063 082) (045 074 100)

11986532

(031 037 044) (050 050 050) (052 060 065) (037 050 063) (039 061 081)

11986533

(015 027 042) (035 040 048) (050 050 050) (035 040 048) (037 051 065)

11986534

(018 037 057) (037 050 063) (052 060 065) (050 050 050) (052 061 068)

11986535

(000 026 055) (019 039 061) (035 049 063) (032 039 048) (050 050 050)

1198654

11986541

11986542

11986543

11986544

11986541

(050 050 050) (042 049 056) (045 062 079) (047 073 100)

11986542

(044 051 058) (050 050 050) (053 063 073) (055 074 094)

11986543

(021 038 055) (027 037 047) (050 050 050) (053 062 071)

11986544

(000 027 053) (006 026 045) (029 038 047) (050 050 050)

1198655

11986551

11986552

11986553

11986554

11986555

11986551

(050 050 050) (064 070 074) (059 071 082) (061 082 100) (042 070 097)

11986552

(026 030 036) (050 050 050) (045 051 057) (047 061 076) (028 050 072)

11986553

(018 029 041) (043 049 055) (050 050 050) (052 060 068) (033 049 065)

11986554

(000 018 039) (024 039 053) (032 040 048) (050 050 050) (031 039 047)

11986555

(003 030 058) (028 050 072) (035 051 067) (053 061 069) (050 050 050)

it probably can mitigate loss for the results In this studywe adopt the five risk dimensions and associated twenty-two risk factors were developed by [4] This can help theproject managers to have an overview of the global pictureof risk Then we apply the Fuzzy LinPreRa method whichcan simplify the Fuzzy AHP method and also avoid thenecessity of checking the consistency in the decision-makingprocess to assess project risk for software developmentBecause in the Fuzzy AHP if there are 119899 criteriaattributesit needs 119899(119899 minus 1)2 pairwise comparisons but the FuzzyLinPreRa just requires 119899 minus 1 comparisons and maintainsthe decision matrices consistency The advantage of applyingFuzzy LinPreRa approach compared with Fuzzy AHP isthat the information demand has been significantly reduced

especially in obtaining information from practitioners Thatis it is more convenient to acquire the judgments of practi-tioners or experts of software development industry througha questionnaire

The evaluation results of the experts in both groupsimplied that the impact degrees of the risk dimensions arethe same whatever the rule on the software developmentproject Although there are some differences in the rankingof risk factors for each risk dimension the results shouldprove to be a valuable reference for software developersAccording to the results of the model built it can be seenthat the proposed model can benefit the stakeholders ofsoftware development projects and help them recognize whatrisk factors they may encounter and to facilitate drawing

8 Mathematical Problems in Engineering

Table 10 Impact degree and ranking of risk dimensions and factors for the two groups

Dimensionsfactors Impact degree of the first group Ranking Impact degree of the second group RankingF1 02481 1 02459 1

F11 03246 1 02968 1F12 01829 4 02134 3F13 02793 2 02784 2F14 02133 3 02114 4

F2 02286 2 02306 2F21 03301 1 02537 2F22 02049 3 02432 3F23 01737 4 01731 4F24 02912 2 03300 1

F3 01749 4 01813 4F31 01261 5 02559 1F32 02266 2 02045 2F33 01688 4 01684 4F34 02520 1 02045 3F35 02265 3 01667 5

F4 01813 3 01894 3F41 02553 3 02930 1F42 02777 1 02945 2F43 02589 2 02325 3F44 02082 4 01800 4

F5 01671 5 01528 5F51 02673 1 02716 1F52 01972 3 01934 3F53 02074 2 01888 4F54 01724 4 01500 5F55 01557 5 01962 2

up project risk management strategies for the adequate allo-cation of resources

References

[1] H M Lee ldquoApplying fuzzy set theory to evaluate the rateof aggregative risk in software developmentrdquo Fuzzy Sets andSystems vol 79 no 3 pp 323ndash336 1996

[2] Y H Kwak and J Stoddard ldquoProject risk management lessonslearned from software development environmentrdquo Technova-tion vol 24 no 11 pp 915ndash920 2004

[3] M de Oliveira Barros C M L Werner and G H TravassosldquoSupporting risks in software project managementrdquoThe Journalof Systems and Software vol 70 no 1-2 pp 21ndash35 2004

[4] S T Lu and SHYu ldquoRisk factors assessment for software devel-opment project based on fuzzy decision makingrdquo InternationalJournal of Information and Electronics Engineering vol 2 no 4pp 596ndash600 2012

[5] T-C Wang and Y-H Chen ldquoApplying fuzzy linguistic prefer-ence relations to the improvement of consistency of fuzzy AHPrdquoInformation Sciences vol 178 no 19 pp 3755ndash3765 2008

[6] E Herrera-Viedma F Herrera F Chiclana and M LuqueldquoSome issues on consistency of fuzzy preference relationsrdquoEuropean Journal of Operational Research vol 154 no 1 pp 98ndash109 2004

[7] B W Boehm ldquoSoftware risk management principles andpracticesrdquo IEEE Software vol 8 no 1 pp 32ndash41 1991

[8] H M Lee and L Lin ldquoFuzzy risk presumptive evaluationin software developmentrdquo International Journal of InnovativeComputing Information and Control vol 7 no 7 pp 3881ndash38892011

[9] J Jiang and G Klein ldquoSoftware development risks to projecteffectivenessrdquo The Journal of Systems and Software vol 52 no1 pp 3ndash10 2000

[10] D X Houston G T Mackulak and J S Collofello ldquoStochasticsimulation of risk factor potential effects for software develop-ment risk managementrdquo The Journal of Systems and Softwarevol 59 no 3 pp 247ndash257 2001

[11] G Buyukozkan and D Ruan ldquoChoquet integral based aggre-gation approach to software development risk assessmentrdquoInformation Sciences vol 180 no 3 pp 441ndash451 2010

[12] X N Lu and Q G Ma ldquoRisk analysis in software developmentproject with owners and contractorsrdquo in Proceedings of the IEEEInternational Engineering Management Conference Innovationand Entrepreneurship for Sustainable Development (IEMC rsquo04)vol 2 pp 789ndash793 October 2004

[13] T L Saaty The Analytic Hierarchy Process McGraw-Hill NewYork NY USA 1980

[14] J J Buckley ldquoRanking alternatives using fuzzy numbersrdquo FuzzySets and Systems vol 15 no 1 pp 21ndash31 1985

Mathematical Problems in Engineering 9

[15] S-J Chen and C-L Hwang Fuzzy Multiple Attribute DecisionMaking-Method and Applications Springer New York NYUSA 1992

[16] T L Saaty and L G Vargas The Logic of Priorities KluwerAcademic Boston Mass USA 1982

[17] T Y Hsieh S T Lu and G H Tzeng ldquoFuzzy MCDM approachfor planning and design tenders selection in public officebuildingsrdquo International Journal of Project Management vol 22no 7 pp 573ndash584 2004

[18] S T Lu ldquoUsing the fuzzy multiple criteria decision makingapproach for risk evaluation on investment of overseas projectrdquoin Proceedings of the 9th International Conference on MachineLearning and Cybernetics (ICMLC rsquo10) vol 4 pp 2031ndash2036July 2010

Submit your manuscripts athttpwwwhindawicom

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Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

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Mathematical PhysicsAdvances in

Complex AnalysisJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

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Discrete Dynamics in Nature and Society

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Discrete MathematicsJournal of

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 5

Table 3 Original evaluation results for the risk dimensions by thesecond group

E1 E2 E3 E4 E5

F1 ES VS VN WK EQ F2

F2 EQ WN VS VS VS F3

F3 ES VS EN AN WN F4

F4 ES WK EQ AB WK F5

Table 4 Original evaluation results for the risk factors by the firstgroup

E1 E2 E3 E4 E5

1198651

F11 VS AB VS EQ AB F12

F12 VN VN VN ES EN F13

F 13 AB WK EQ ES WK F14

1198652

11986521

VS AB VS WK ES F22

11986522

VS EQ WK WK EN F23

11986523

AN VN EN EQ VN F24

1198653

F31 AN VN EQ VN AN F32

F32 VS VS WK VN AB F33

F33 AN AN VN AN VS F34

F34 EQ VS AB EQ VN F35

1198654

F41 EQ EN EQ WN EQ F42

F42 VS VN VN ES VS F43

F43 EQ ES WK VS WN F44

1198655

F51 VS AB AB VS ES F52

F52 EQ VS WN VN EN F53

F53 EQ VS ES ES ES F54

F54 VS VN WK VS EQ F55

survey and were asked to compare the relative degree ofimpact for the risk dimensions and factors identified inthis study in pairwise sequential order That is they onlyneeded to compare the relative impact degree from 119865

1to

1198652 from 119865

2to 1198653 from 119865

3to 1198654 from 119865

4to 1198655 from 119865

11

to 11986512 from 119865

12to 11986513 and so on Tables 2 and 3 list the

original evaluation results of this pairwise comparison for therisk dimensions given by the five experts of the two groupsSimilarly Tables 4 and 5 display the original pairwise compar-ison matrix for the twenty-two risk factors given by the twogroups Since the preferences and experiences of these expertsare different we use the fuzzy linguistic assessment variablesas in Table 1 and from (3) to (5) to aggregate the expertsrsquosubjective judgments toward the impact of the degree of riskdimensions and factors yielding the synthesized triangularfuzzy numbers listed in Tables 6 7 8 and 9 respectively Theranking of the impact degree is determined by constructinga crisp value from the fuzzy number Hence defuzzificationneeds to be performed to arrange the fuzzy numbers for

Table 5Original evaluation results for the risk factors by the secondgroup

E1 E2 E3 E4 E5

1198651

F11 VS ES EQ VS WK F12

F12 WN EN EQ VN EN F13

F13 ES ES EQ VS ES F14

1198652

F21 WN EN EQ AB WN F22

F22 ES ES VS VS VN F23

F23 EN VN AN AN EN F24

1198653

11986531

ES VS VN AB VS F32

11986532

ES WK VS AB VN F33

11986533

WN EN EQ AN EQ F34

11986534

ES ES EQ AB EQ F35

1198654

F41 WK ES EQ AN WK F42

F42 ES ES ES VS EQ F43

F43 ES ES EQ VS WK F44

1198655

F51 VS VS AB AB ES F52

F52 EQ EN EQ VS WN F53

F53 EQ ES EQ VS ES F54

F54 EN EN VN EN WN F55

ranking Table 10 lists the impact degree and ranking of riskdimensions and factors for software development projectsobtained by using (6) and (7)

For experts in the first group who are staff members of atechnology enterprise among the identified five dimensionsldquoorganization function riskrdquo was found to be the mostimportant risk dimension to influence software developmentperformance and success ldquoDeveloping technology riskrdquo andldquoresources integration riskrdquo are respectively the second andthird highest impact dimensions affecting software devel-opment project performance ldquoPersonnel system riskrdquo andldquosystem requirement riskrdquo are the last two dimensions insequence in relative importance affecting performance andsuccess of the software development project

For each dimension among the first risk dimensions (1198651)

incapable organizationmanagement (11986511) was considered the

most impact risk factor and it is also the most importantfactor for the global aspect Among the second fourth andfifth dimensions (ie 119865

2 1198654 and 119865

5) immature technology

development (11986521) improper coordination with related divi-

sions (11986542) and continuing stream of requirements changes

(11986551) were all found to be the highest impact risk fac-

tors influencing the software development project successUnavailability of key staff or project managers (119865

32) and

lack of staff commitment and low morale (11986534) respectively

are the most observed prominent risk factors which harmsoftware development project success in each dimension

The points of view in relation to the risk dimensionsexpressed by the experts of the second group who are staff

6 Mathematical Problems in Engineering

Table 6 Aggregation decision matrix of the risk dimensions form the first group

1198651

1198652

1198653

1198654

1198655

1198651

(050 050 050) (047 054 062) (054 069 081) (046 068 087) (041 072 100)

1198652

(038 046 053) (050 050 050) (057 065 069) (049 063 075) (044 068 088)

1198653

(019 031 046) (031 035 043) (050 050 050) (041 049 056) (037 053 069)

1198654

(013 032 054) (025 037 051) (044 051 059) (050 050 050) (046 054 063)

1198655

(000 028 059) (012 032 056) (031 047 063) (037 046 054) (050 050 050)

Table 7 Aggregation decision matrix of the risk factors from the first group

1198651

11986511

11986512

11986513

11986514

11986511

(050 050 050) (072 080 085) (040 060 077) (045 075 100)

11986512

(015 020 028) (050 050 050) (018 030 042) (023 045 065)

11986513

(023 040 060) (058 070 082) (050 050 050) (055 065 073)

11986514

(000 025 055) (035 055 077) (027 035 045) (050 050 050)

1198652

11986521

11986522

11986523

11986524

11986521

(050 050 050) (066 076 084) (063 082 100) (031 058 085)

11986522

(016 024 034) (050 050 050) (047 056 066) (015 032 052)

11986523

(000 018 037) (034 044 053) (050 050 050) (018 026 035)

11986524

(015 042 069) (048 068 085) (065 074 082) (050 050 050)

1198653

11986531

11986532

11986533

11986534

11986535

11986531

(050 050 050) (018 023 030) (026 038 052) (000 015 036) (000 023 050)

11986532

(070 077 082) (050 050 050) (058 065 071) (032 042 056) (032 050 070)

11986533

(048 062 074) (029 035 042) (050 050 050) (024 027 035) (024 035 048)

11986534

(064 085 100) (044 058 068) (065 073 076) (050 050 050) (050 058 064)

11986535

(050 077 100) (030 050 068) (052 065 076) (036 042 050) (050 050 050)

1198654

11986541

11986542

11986543

11986544

11986541

(050 050 050) (032 044 056) (024 048 072) (024 060 096)

11986542

(044 056 068) (050 050 050) (042 054 066) (042 066 090)

11986543

(028 052 076) (034 046 058) (050 050 050) (050 062 074)

11986544

(004 040 076) (010 034 058) (026 038 050) (050 050 050)

1198655

11986551

11986552

11986553

11986554

11986555

11986551

(050 050 050) (063 068 072) (055 065 075) (056 075 091) (056 079 100)

11986552

(028 032 037) (050 050 050) (042 047 053) (044 056 069) (044 061 078)

11986553

(025 035 045) (047 053 058) (050 050 050) (052 059 066) (052 064 075)

11986554

(009 025 044) (031 044 056) (034 041 048) (050 050 050) (050 055 059)

11986555

(000 021 044) (022 039 056) (025 036 048) (041 045 050) (050 050 050)

members of a software development company are the same asthe first group For each dimension the ranking results of theimpact degree for risk factors are somewhat different from thefirst group For example among the first risk dimension (119865

1)

incapable organization management (11986511) is also considered

as the most impacting risk factor in the first group but itis the factor having the second greatest impact for globalaspects which is not the same as the first group The mostdifference in ranking for factors of dimensions between thesetwo groups was for the third risk dimension (119865

3) The second

group considers reliance on a few key personnel (11986531) as the

most important factor in the ldquopersonnel system riskrdquo aspectbut it has the least impact based on the evaluations of the firstgroup

According to the results of this case study whether it istechnology enterprise (demander) or software development

company (supplier) they should realize that organization andcommunicationmanagement is the upmost restrict conditionfor the success of software development project that isorganizational culture organizational structure organiza-tional processes organizationrsquos established communicationschannels and so forth The internal and external enterpriseenvironmental factors will critically influence the perfor-mance of the software development project It indicates thatthe application of appropriate project management skills andknowledge is necessary

5 Conclusions

There is an old saying that goes ldquoAn ounce of preventionis worth a pound of curerdquo Therefore if we can understandthe encountered risks and pay more attention in advance

Mathematical Problems in Engineering 7

Table 8 Aggregation decision matrix of the risk dimensions from the second group

1198651

1198652

1198653

1198654

1198655

1198651

(050 050 050) (047 053 060) (053 066 078) (044 064 084) (048 074 100)

1198652

(040 047 053) (050 050 050) (057 063 068) (048 060 074) (051 070 090)

1198653

(022 034 047) (032 038 043) (050 050 050) (041 048 056) (044 058 072)

1198654

(016 036 056) (026 040 052) (044 052 059) (050 050 050) (053 060 066)

1198655

(000 026 052) (010 030 049) (028 042 056) (034 040 047) (050 050 050)

Table 9 Aggregation decision matrix of the risk factors from the second group

1198651

11986511

11986512

11986513

11986514

11986511

(050 050 050) (058 067 076) (033 053 073) (036 068 100)

11986512

(024 033 042) (050 050 050) (026 036 047) (029 052 074)

11986513

(027 047 067) (053 064 074) (050 050 050) (053 065 077)

11986514

(000 032 064) (026 048 071) (023 035 047) (050 050 050)

1198652

11986521

11986522

11986523

11986524

11986521

(050 050 050) (041 052 061) (043 067 089) (000 033 069)

11986522

(039 048 059) (050 050 050) (052 065 078) (009 031 057)

11986523

(011 033 057) (022 035 048) (050 050 050) (007 017 030)

11986524

(031 067 100) (043 069 091) (070 083 093) (050 050 050)

1198653

11986531

11986532

11986533

11986534

11986535

11986531

(050 050 050) (056 063 069) (058 073 085) (043 063 082) (045 074 100)

11986532

(031 037 044) (050 050 050) (052 060 065) (037 050 063) (039 061 081)

11986533

(015 027 042) (035 040 048) (050 050 050) (035 040 048) (037 051 065)

11986534

(018 037 057) (037 050 063) (052 060 065) (050 050 050) (052 061 068)

11986535

(000 026 055) (019 039 061) (035 049 063) (032 039 048) (050 050 050)

1198654

11986541

11986542

11986543

11986544

11986541

(050 050 050) (042 049 056) (045 062 079) (047 073 100)

11986542

(044 051 058) (050 050 050) (053 063 073) (055 074 094)

11986543

(021 038 055) (027 037 047) (050 050 050) (053 062 071)

11986544

(000 027 053) (006 026 045) (029 038 047) (050 050 050)

1198655

11986551

11986552

11986553

11986554

11986555

11986551

(050 050 050) (064 070 074) (059 071 082) (061 082 100) (042 070 097)

11986552

(026 030 036) (050 050 050) (045 051 057) (047 061 076) (028 050 072)

11986553

(018 029 041) (043 049 055) (050 050 050) (052 060 068) (033 049 065)

11986554

(000 018 039) (024 039 053) (032 040 048) (050 050 050) (031 039 047)

11986555

(003 030 058) (028 050 072) (035 051 067) (053 061 069) (050 050 050)

it probably can mitigate loss for the results In this studywe adopt the five risk dimensions and associated twenty-two risk factors were developed by [4] This can help theproject managers to have an overview of the global pictureof risk Then we apply the Fuzzy LinPreRa method whichcan simplify the Fuzzy AHP method and also avoid thenecessity of checking the consistency in the decision-makingprocess to assess project risk for software developmentBecause in the Fuzzy AHP if there are 119899 criteriaattributesit needs 119899(119899 minus 1)2 pairwise comparisons but the FuzzyLinPreRa just requires 119899 minus 1 comparisons and maintainsthe decision matrices consistency The advantage of applyingFuzzy LinPreRa approach compared with Fuzzy AHP isthat the information demand has been significantly reduced

especially in obtaining information from practitioners Thatis it is more convenient to acquire the judgments of practi-tioners or experts of software development industry througha questionnaire

The evaluation results of the experts in both groupsimplied that the impact degrees of the risk dimensions arethe same whatever the rule on the software developmentproject Although there are some differences in the rankingof risk factors for each risk dimension the results shouldprove to be a valuable reference for software developersAccording to the results of the model built it can be seenthat the proposed model can benefit the stakeholders ofsoftware development projects and help them recognize whatrisk factors they may encounter and to facilitate drawing

8 Mathematical Problems in Engineering

Table 10 Impact degree and ranking of risk dimensions and factors for the two groups

Dimensionsfactors Impact degree of the first group Ranking Impact degree of the second group RankingF1 02481 1 02459 1

F11 03246 1 02968 1F12 01829 4 02134 3F13 02793 2 02784 2F14 02133 3 02114 4

F2 02286 2 02306 2F21 03301 1 02537 2F22 02049 3 02432 3F23 01737 4 01731 4F24 02912 2 03300 1

F3 01749 4 01813 4F31 01261 5 02559 1F32 02266 2 02045 2F33 01688 4 01684 4F34 02520 1 02045 3F35 02265 3 01667 5

F4 01813 3 01894 3F41 02553 3 02930 1F42 02777 1 02945 2F43 02589 2 02325 3F44 02082 4 01800 4

F5 01671 5 01528 5F51 02673 1 02716 1F52 01972 3 01934 3F53 02074 2 01888 4F54 01724 4 01500 5F55 01557 5 01962 2

up project risk management strategies for the adequate allo-cation of resources

References

[1] H M Lee ldquoApplying fuzzy set theory to evaluate the rateof aggregative risk in software developmentrdquo Fuzzy Sets andSystems vol 79 no 3 pp 323ndash336 1996

[2] Y H Kwak and J Stoddard ldquoProject risk management lessonslearned from software development environmentrdquo Technova-tion vol 24 no 11 pp 915ndash920 2004

[3] M de Oliveira Barros C M L Werner and G H TravassosldquoSupporting risks in software project managementrdquoThe Journalof Systems and Software vol 70 no 1-2 pp 21ndash35 2004

[4] S T Lu and SHYu ldquoRisk factors assessment for software devel-opment project based on fuzzy decision makingrdquo InternationalJournal of Information and Electronics Engineering vol 2 no 4pp 596ndash600 2012

[5] T-C Wang and Y-H Chen ldquoApplying fuzzy linguistic prefer-ence relations to the improvement of consistency of fuzzy AHPrdquoInformation Sciences vol 178 no 19 pp 3755ndash3765 2008

[6] E Herrera-Viedma F Herrera F Chiclana and M LuqueldquoSome issues on consistency of fuzzy preference relationsrdquoEuropean Journal of Operational Research vol 154 no 1 pp 98ndash109 2004

[7] B W Boehm ldquoSoftware risk management principles andpracticesrdquo IEEE Software vol 8 no 1 pp 32ndash41 1991

[8] H M Lee and L Lin ldquoFuzzy risk presumptive evaluationin software developmentrdquo International Journal of InnovativeComputing Information and Control vol 7 no 7 pp 3881ndash38892011

[9] J Jiang and G Klein ldquoSoftware development risks to projecteffectivenessrdquo The Journal of Systems and Software vol 52 no1 pp 3ndash10 2000

[10] D X Houston G T Mackulak and J S Collofello ldquoStochasticsimulation of risk factor potential effects for software develop-ment risk managementrdquo The Journal of Systems and Softwarevol 59 no 3 pp 247ndash257 2001

[11] G Buyukozkan and D Ruan ldquoChoquet integral based aggre-gation approach to software development risk assessmentrdquoInformation Sciences vol 180 no 3 pp 441ndash451 2010

[12] X N Lu and Q G Ma ldquoRisk analysis in software developmentproject with owners and contractorsrdquo in Proceedings of the IEEEInternational Engineering Management Conference Innovationand Entrepreneurship for Sustainable Development (IEMC rsquo04)vol 2 pp 789ndash793 October 2004

[13] T L Saaty The Analytic Hierarchy Process McGraw-Hill NewYork NY USA 1980

[14] J J Buckley ldquoRanking alternatives using fuzzy numbersrdquo FuzzySets and Systems vol 15 no 1 pp 21ndash31 1985

Mathematical Problems in Engineering 9

[15] S-J Chen and C-L Hwang Fuzzy Multiple Attribute DecisionMaking-Method and Applications Springer New York NYUSA 1992

[16] T L Saaty and L G Vargas The Logic of Priorities KluwerAcademic Boston Mass USA 1982

[17] T Y Hsieh S T Lu and G H Tzeng ldquoFuzzy MCDM approachfor planning and design tenders selection in public officebuildingsrdquo International Journal of Project Management vol 22no 7 pp 573ndash584 2004

[18] S T Lu ldquoUsing the fuzzy multiple criteria decision makingapproach for risk evaluation on investment of overseas projectrdquoin Proceedings of the 9th International Conference on MachineLearning and Cybernetics (ICMLC rsquo10) vol 4 pp 2031ndash2036July 2010

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Mathematical Problems in Engineering

Table 6 Aggregation decision matrix of the risk dimensions form the first group

1198651

1198652

1198653

1198654

1198655

1198651

(050 050 050) (047 054 062) (054 069 081) (046 068 087) (041 072 100)

1198652

(038 046 053) (050 050 050) (057 065 069) (049 063 075) (044 068 088)

1198653

(019 031 046) (031 035 043) (050 050 050) (041 049 056) (037 053 069)

1198654

(013 032 054) (025 037 051) (044 051 059) (050 050 050) (046 054 063)

1198655

(000 028 059) (012 032 056) (031 047 063) (037 046 054) (050 050 050)

Table 7 Aggregation decision matrix of the risk factors from the first group

1198651

11986511

11986512

11986513

11986514

11986511

(050 050 050) (072 080 085) (040 060 077) (045 075 100)

11986512

(015 020 028) (050 050 050) (018 030 042) (023 045 065)

11986513

(023 040 060) (058 070 082) (050 050 050) (055 065 073)

11986514

(000 025 055) (035 055 077) (027 035 045) (050 050 050)

1198652

11986521

11986522

11986523

11986524

11986521

(050 050 050) (066 076 084) (063 082 100) (031 058 085)

11986522

(016 024 034) (050 050 050) (047 056 066) (015 032 052)

11986523

(000 018 037) (034 044 053) (050 050 050) (018 026 035)

11986524

(015 042 069) (048 068 085) (065 074 082) (050 050 050)

1198653

11986531

11986532

11986533

11986534

11986535

11986531

(050 050 050) (018 023 030) (026 038 052) (000 015 036) (000 023 050)

11986532

(070 077 082) (050 050 050) (058 065 071) (032 042 056) (032 050 070)

11986533

(048 062 074) (029 035 042) (050 050 050) (024 027 035) (024 035 048)

11986534

(064 085 100) (044 058 068) (065 073 076) (050 050 050) (050 058 064)

11986535

(050 077 100) (030 050 068) (052 065 076) (036 042 050) (050 050 050)

1198654

11986541

11986542

11986543

11986544

11986541

(050 050 050) (032 044 056) (024 048 072) (024 060 096)

11986542

(044 056 068) (050 050 050) (042 054 066) (042 066 090)

11986543

(028 052 076) (034 046 058) (050 050 050) (050 062 074)

11986544

(004 040 076) (010 034 058) (026 038 050) (050 050 050)

1198655

11986551

11986552

11986553

11986554

11986555

11986551

(050 050 050) (063 068 072) (055 065 075) (056 075 091) (056 079 100)

11986552

(028 032 037) (050 050 050) (042 047 053) (044 056 069) (044 061 078)

11986553

(025 035 045) (047 053 058) (050 050 050) (052 059 066) (052 064 075)

11986554

(009 025 044) (031 044 056) (034 041 048) (050 050 050) (050 055 059)

11986555

(000 021 044) (022 039 056) (025 036 048) (041 045 050) (050 050 050)

members of a software development company are the same asthe first group For each dimension the ranking results of theimpact degree for risk factors are somewhat different from thefirst group For example among the first risk dimension (119865

1)

incapable organization management (11986511) is also considered

as the most impacting risk factor in the first group but itis the factor having the second greatest impact for globalaspects which is not the same as the first group The mostdifference in ranking for factors of dimensions between thesetwo groups was for the third risk dimension (119865

3) The second

group considers reliance on a few key personnel (11986531) as the

most important factor in the ldquopersonnel system riskrdquo aspectbut it has the least impact based on the evaluations of the firstgroup

According to the results of this case study whether it istechnology enterprise (demander) or software development

company (supplier) they should realize that organization andcommunicationmanagement is the upmost restrict conditionfor the success of software development project that isorganizational culture organizational structure organiza-tional processes organizationrsquos established communicationschannels and so forth The internal and external enterpriseenvironmental factors will critically influence the perfor-mance of the software development project It indicates thatthe application of appropriate project management skills andknowledge is necessary

5 Conclusions

There is an old saying that goes ldquoAn ounce of preventionis worth a pound of curerdquo Therefore if we can understandthe encountered risks and pay more attention in advance

Mathematical Problems in Engineering 7

Table 8 Aggregation decision matrix of the risk dimensions from the second group

1198651

1198652

1198653

1198654

1198655

1198651

(050 050 050) (047 053 060) (053 066 078) (044 064 084) (048 074 100)

1198652

(040 047 053) (050 050 050) (057 063 068) (048 060 074) (051 070 090)

1198653

(022 034 047) (032 038 043) (050 050 050) (041 048 056) (044 058 072)

1198654

(016 036 056) (026 040 052) (044 052 059) (050 050 050) (053 060 066)

1198655

(000 026 052) (010 030 049) (028 042 056) (034 040 047) (050 050 050)

Table 9 Aggregation decision matrix of the risk factors from the second group

1198651

11986511

11986512

11986513

11986514

11986511

(050 050 050) (058 067 076) (033 053 073) (036 068 100)

11986512

(024 033 042) (050 050 050) (026 036 047) (029 052 074)

11986513

(027 047 067) (053 064 074) (050 050 050) (053 065 077)

11986514

(000 032 064) (026 048 071) (023 035 047) (050 050 050)

1198652

11986521

11986522

11986523

11986524

11986521

(050 050 050) (041 052 061) (043 067 089) (000 033 069)

11986522

(039 048 059) (050 050 050) (052 065 078) (009 031 057)

11986523

(011 033 057) (022 035 048) (050 050 050) (007 017 030)

11986524

(031 067 100) (043 069 091) (070 083 093) (050 050 050)

1198653

11986531

11986532

11986533

11986534

11986535

11986531

(050 050 050) (056 063 069) (058 073 085) (043 063 082) (045 074 100)

11986532

(031 037 044) (050 050 050) (052 060 065) (037 050 063) (039 061 081)

11986533

(015 027 042) (035 040 048) (050 050 050) (035 040 048) (037 051 065)

11986534

(018 037 057) (037 050 063) (052 060 065) (050 050 050) (052 061 068)

11986535

(000 026 055) (019 039 061) (035 049 063) (032 039 048) (050 050 050)

1198654

11986541

11986542

11986543

11986544

11986541

(050 050 050) (042 049 056) (045 062 079) (047 073 100)

11986542

(044 051 058) (050 050 050) (053 063 073) (055 074 094)

11986543

(021 038 055) (027 037 047) (050 050 050) (053 062 071)

11986544

(000 027 053) (006 026 045) (029 038 047) (050 050 050)

1198655

11986551

11986552

11986553

11986554

11986555

11986551

(050 050 050) (064 070 074) (059 071 082) (061 082 100) (042 070 097)

11986552

(026 030 036) (050 050 050) (045 051 057) (047 061 076) (028 050 072)

11986553

(018 029 041) (043 049 055) (050 050 050) (052 060 068) (033 049 065)

11986554

(000 018 039) (024 039 053) (032 040 048) (050 050 050) (031 039 047)

11986555

(003 030 058) (028 050 072) (035 051 067) (053 061 069) (050 050 050)

it probably can mitigate loss for the results In this studywe adopt the five risk dimensions and associated twenty-two risk factors were developed by [4] This can help theproject managers to have an overview of the global pictureof risk Then we apply the Fuzzy LinPreRa method whichcan simplify the Fuzzy AHP method and also avoid thenecessity of checking the consistency in the decision-makingprocess to assess project risk for software developmentBecause in the Fuzzy AHP if there are 119899 criteriaattributesit needs 119899(119899 minus 1)2 pairwise comparisons but the FuzzyLinPreRa just requires 119899 minus 1 comparisons and maintainsthe decision matrices consistency The advantage of applyingFuzzy LinPreRa approach compared with Fuzzy AHP isthat the information demand has been significantly reduced

especially in obtaining information from practitioners Thatis it is more convenient to acquire the judgments of practi-tioners or experts of software development industry througha questionnaire

The evaluation results of the experts in both groupsimplied that the impact degrees of the risk dimensions arethe same whatever the rule on the software developmentproject Although there are some differences in the rankingof risk factors for each risk dimension the results shouldprove to be a valuable reference for software developersAccording to the results of the model built it can be seenthat the proposed model can benefit the stakeholders ofsoftware development projects and help them recognize whatrisk factors they may encounter and to facilitate drawing

8 Mathematical Problems in Engineering

Table 10 Impact degree and ranking of risk dimensions and factors for the two groups

Dimensionsfactors Impact degree of the first group Ranking Impact degree of the second group RankingF1 02481 1 02459 1

F11 03246 1 02968 1F12 01829 4 02134 3F13 02793 2 02784 2F14 02133 3 02114 4

F2 02286 2 02306 2F21 03301 1 02537 2F22 02049 3 02432 3F23 01737 4 01731 4F24 02912 2 03300 1

F3 01749 4 01813 4F31 01261 5 02559 1F32 02266 2 02045 2F33 01688 4 01684 4F34 02520 1 02045 3F35 02265 3 01667 5

F4 01813 3 01894 3F41 02553 3 02930 1F42 02777 1 02945 2F43 02589 2 02325 3F44 02082 4 01800 4

F5 01671 5 01528 5F51 02673 1 02716 1F52 01972 3 01934 3F53 02074 2 01888 4F54 01724 4 01500 5F55 01557 5 01962 2

up project risk management strategies for the adequate allo-cation of resources

References

[1] H M Lee ldquoApplying fuzzy set theory to evaluate the rateof aggregative risk in software developmentrdquo Fuzzy Sets andSystems vol 79 no 3 pp 323ndash336 1996

[2] Y H Kwak and J Stoddard ldquoProject risk management lessonslearned from software development environmentrdquo Technova-tion vol 24 no 11 pp 915ndash920 2004

[3] M de Oliveira Barros C M L Werner and G H TravassosldquoSupporting risks in software project managementrdquoThe Journalof Systems and Software vol 70 no 1-2 pp 21ndash35 2004

[4] S T Lu and SHYu ldquoRisk factors assessment for software devel-opment project based on fuzzy decision makingrdquo InternationalJournal of Information and Electronics Engineering vol 2 no 4pp 596ndash600 2012

[5] T-C Wang and Y-H Chen ldquoApplying fuzzy linguistic prefer-ence relations to the improvement of consistency of fuzzy AHPrdquoInformation Sciences vol 178 no 19 pp 3755ndash3765 2008

[6] E Herrera-Viedma F Herrera F Chiclana and M LuqueldquoSome issues on consistency of fuzzy preference relationsrdquoEuropean Journal of Operational Research vol 154 no 1 pp 98ndash109 2004

[7] B W Boehm ldquoSoftware risk management principles andpracticesrdquo IEEE Software vol 8 no 1 pp 32ndash41 1991

[8] H M Lee and L Lin ldquoFuzzy risk presumptive evaluationin software developmentrdquo International Journal of InnovativeComputing Information and Control vol 7 no 7 pp 3881ndash38892011

[9] J Jiang and G Klein ldquoSoftware development risks to projecteffectivenessrdquo The Journal of Systems and Software vol 52 no1 pp 3ndash10 2000

[10] D X Houston G T Mackulak and J S Collofello ldquoStochasticsimulation of risk factor potential effects for software develop-ment risk managementrdquo The Journal of Systems and Softwarevol 59 no 3 pp 247ndash257 2001

[11] G Buyukozkan and D Ruan ldquoChoquet integral based aggre-gation approach to software development risk assessmentrdquoInformation Sciences vol 180 no 3 pp 441ndash451 2010

[12] X N Lu and Q G Ma ldquoRisk analysis in software developmentproject with owners and contractorsrdquo in Proceedings of the IEEEInternational Engineering Management Conference Innovationand Entrepreneurship for Sustainable Development (IEMC rsquo04)vol 2 pp 789ndash793 October 2004

[13] T L Saaty The Analytic Hierarchy Process McGraw-Hill NewYork NY USA 1980

[14] J J Buckley ldquoRanking alternatives using fuzzy numbersrdquo FuzzySets and Systems vol 15 no 1 pp 21ndash31 1985

Mathematical Problems in Engineering 9

[15] S-J Chen and C-L Hwang Fuzzy Multiple Attribute DecisionMaking-Method and Applications Springer New York NYUSA 1992

[16] T L Saaty and L G Vargas The Logic of Priorities KluwerAcademic Boston Mass USA 1982

[17] T Y Hsieh S T Lu and G H Tzeng ldquoFuzzy MCDM approachfor planning and design tenders selection in public officebuildingsrdquo International Journal of Project Management vol 22no 7 pp 573ndash584 2004

[18] S T Lu ldquoUsing the fuzzy multiple criteria decision makingapproach for risk evaluation on investment of overseas projectrdquoin Proceedings of the 9th International Conference on MachineLearning and Cybernetics (ICMLC rsquo10) vol 4 pp 2031ndash2036July 2010

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 7

Table 8 Aggregation decision matrix of the risk dimensions from the second group

1198651

1198652

1198653

1198654

1198655

1198651

(050 050 050) (047 053 060) (053 066 078) (044 064 084) (048 074 100)

1198652

(040 047 053) (050 050 050) (057 063 068) (048 060 074) (051 070 090)

1198653

(022 034 047) (032 038 043) (050 050 050) (041 048 056) (044 058 072)

1198654

(016 036 056) (026 040 052) (044 052 059) (050 050 050) (053 060 066)

1198655

(000 026 052) (010 030 049) (028 042 056) (034 040 047) (050 050 050)

Table 9 Aggregation decision matrix of the risk factors from the second group

1198651

11986511

11986512

11986513

11986514

11986511

(050 050 050) (058 067 076) (033 053 073) (036 068 100)

11986512

(024 033 042) (050 050 050) (026 036 047) (029 052 074)

11986513

(027 047 067) (053 064 074) (050 050 050) (053 065 077)

11986514

(000 032 064) (026 048 071) (023 035 047) (050 050 050)

1198652

11986521

11986522

11986523

11986524

11986521

(050 050 050) (041 052 061) (043 067 089) (000 033 069)

11986522

(039 048 059) (050 050 050) (052 065 078) (009 031 057)

11986523

(011 033 057) (022 035 048) (050 050 050) (007 017 030)

11986524

(031 067 100) (043 069 091) (070 083 093) (050 050 050)

1198653

11986531

11986532

11986533

11986534

11986535

11986531

(050 050 050) (056 063 069) (058 073 085) (043 063 082) (045 074 100)

11986532

(031 037 044) (050 050 050) (052 060 065) (037 050 063) (039 061 081)

11986533

(015 027 042) (035 040 048) (050 050 050) (035 040 048) (037 051 065)

11986534

(018 037 057) (037 050 063) (052 060 065) (050 050 050) (052 061 068)

11986535

(000 026 055) (019 039 061) (035 049 063) (032 039 048) (050 050 050)

1198654

11986541

11986542

11986543

11986544

11986541

(050 050 050) (042 049 056) (045 062 079) (047 073 100)

11986542

(044 051 058) (050 050 050) (053 063 073) (055 074 094)

11986543

(021 038 055) (027 037 047) (050 050 050) (053 062 071)

11986544

(000 027 053) (006 026 045) (029 038 047) (050 050 050)

1198655

11986551

11986552

11986553

11986554

11986555

11986551

(050 050 050) (064 070 074) (059 071 082) (061 082 100) (042 070 097)

11986552

(026 030 036) (050 050 050) (045 051 057) (047 061 076) (028 050 072)

11986553

(018 029 041) (043 049 055) (050 050 050) (052 060 068) (033 049 065)

11986554

(000 018 039) (024 039 053) (032 040 048) (050 050 050) (031 039 047)

11986555

(003 030 058) (028 050 072) (035 051 067) (053 061 069) (050 050 050)

it probably can mitigate loss for the results In this studywe adopt the five risk dimensions and associated twenty-two risk factors were developed by [4] This can help theproject managers to have an overview of the global pictureof risk Then we apply the Fuzzy LinPreRa method whichcan simplify the Fuzzy AHP method and also avoid thenecessity of checking the consistency in the decision-makingprocess to assess project risk for software developmentBecause in the Fuzzy AHP if there are 119899 criteriaattributesit needs 119899(119899 minus 1)2 pairwise comparisons but the FuzzyLinPreRa just requires 119899 minus 1 comparisons and maintainsthe decision matrices consistency The advantage of applyingFuzzy LinPreRa approach compared with Fuzzy AHP isthat the information demand has been significantly reduced

especially in obtaining information from practitioners Thatis it is more convenient to acquire the judgments of practi-tioners or experts of software development industry througha questionnaire

The evaluation results of the experts in both groupsimplied that the impact degrees of the risk dimensions arethe same whatever the rule on the software developmentproject Although there are some differences in the rankingof risk factors for each risk dimension the results shouldprove to be a valuable reference for software developersAccording to the results of the model built it can be seenthat the proposed model can benefit the stakeholders ofsoftware development projects and help them recognize whatrisk factors they may encounter and to facilitate drawing

8 Mathematical Problems in Engineering

Table 10 Impact degree and ranking of risk dimensions and factors for the two groups

Dimensionsfactors Impact degree of the first group Ranking Impact degree of the second group RankingF1 02481 1 02459 1

F11 03246 1 02968 1F12 01829 4 02134 3F13 02793 2 02784 2F14 02133 3 02114 4

F2 02286 2 02306 2F21 03301 1 02537 2F22 02049 3 02432 3F23 01737 4 01731 4F24 02912 2 03300 1

F3 01749 4 01813 4F31 01261 5 02559 1F32 02266 2 02045 2F33 01688 4 01684 4F34 02520 1 02045 3F35 02265 3 01667 5

F4 01813 3 01894 3F41 02553 3 02930 1F42 02777 1 02945 2F43 02589 2 02325 3F44 02082 4 01800 4

F5 01671 5 01528 5F51 02673 1 02716 1F52 01972 3 01934 3F53 02074 2 01888 4F54 01724 4 01500 5F55 01557 5 01962 2

up project risk management strategies for the adequate allo-cation of resources

References

[1] H M Lee ldquoApplying fuzzy set theory to evaluate the rateof aggregative risk in software developmentrdquo Fuzzy Sets andSystems vol 79 no 3 pp 323ndash336 1996

[2] Y H Kwak and J Stoddard ldquoProject risk management lessonslearned from software development environmentrdquo Technova-tion vol 24 no 11 pp 915ndash920 2004

[3] M de Oliveira Barros C M L Werner and G H TravassosldquoSupporting risks in software project managementrdquoThe Journalof Systems and Software vol 70 no 1-2 pp 21ndash35 2004

[4] S T Lu and SHYu ldquoRisk factors assessment for software devel-opment project based on fuzzy decision makingrdquo InternationalJournal of Information and Electronics Engineering vol 2 no 4pp 596ndash600 2012

[5] T-C Wang and Y-H Chen ldquoApplying fuzzy linguistic prefer-ence relations to the improvement of consistency of fuzzy AHPrdquoInformation Sciences vol 178 no 19 pp 3755ndash3765 2008

[6] E Herrera-Viedma F Herrera F Chiclana and M LuqueldquoSome issues on consistency of fuzzy preference relationsrdquoEuropean Journal of Operational Research vol 154 no 1 pp 98ndash109 2004

[7] B W Boehm ldquoSoftware risk management principles andpracticesrdquo IEEE Software vol 8 no 1 pp 32ndash41 1991

[8] H M Lee and L Lin ldquoFuzzy risk presumptive evaluationin software developmentrdquo International Journal of InnovativeComputing Information and Control vol 7 no 7 pp 3881ndash38892011

[9] J Jiang and G Klein ldquoSoftware development risks to projecteffectivenessrdquo The Journal of Systems and Software vol 52 no1 pp 3ndash10 2000

[10] D X Houston G T Mackulak and J S Collofello ldquoStochasticsimulation of risk factor potential effects for software develop-ment risk managementrdquo The Journal of Systems and Softwarevol 59 no 3 pp 247ndash257 2001

[11] G Buyukozkan and D Ruan ldquoChoquet integral based aggre-gation approach to software development risk assessmentrdquoInformation Sciences vol 180 no 3 pp 441ndash451 2010

[12] X N Lu and Q G Ma ldquoRisk analysis in software developmentproject with owners and contractorsrdquo in Proceedings of the IEEEInternational Engineering Management Conference Innovationand Entrepreneurship for Sustainable Development (IEMC rsquo04)vol 2 pp 789ndash793 October 2004

[13] T L Saaty The Analytic Hierarchy Process McGraw-Hill NewYork NY USA 1980

[14] J J Buckley ldquoRanking alternatives using fuzzy numbersrdquo FuzzySets and Systems vol 15 no 1 pp 21ndash31 1985

Mathematical Problems in Engineering 9

[15] S-J Chen and C-L Hwang Fuzzy Multiple Attribute DecisionMaking-Method and Applications Springer New York NYUSA 1992

[16] T L Saaty and L G Vargas The Logic of Priorities KluwerAcademic Boston Mass USA 1982

[17] T Y Hsieh S T Lu and G H Tzeng ldquoFuzzy MCDM approachfor planning and design tenders selection in public officebuildingsrdquo International Journal of Project Management vol 22no 7 pp 573ndash584 2004

[18] S T Lu ldquoUsing the fuzzy multiple criteria decision makingapproach for risk evaluation on investment of overseas projectrdquoin Proceedings of the 9th International Conference on MachineLearning and Cybernetics (ICMLC rsquo10) vol 4 pp 2031ndash2036July 2010

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Mathematical Problems in Engineering

Table 10 Impact degree and ranking of risk dimensions and factors for the two groups

Dimensionsfactors Impact degree of the first group Ranking Impact degree of the second group RankingF1 02481 1 02459 1

F11 03246 1 02968 1F12 01829 4 02134 3F13 02793 2 02784 2F14 02133 3 02114 4

F2 02286 2 02306 2F21 03301 1 02537 2F22 02049 3 02432 3F23 01737 4 01731 4F24 02912 2 03300 1

F3 01749 4 01813 4F31 01261 5 02559 1F32 02266 2 02045 2F33 01688 4 01684 4F34 02520 1 02045 3F35 02265 3 01667 5

F4 01813 3 01894 3F41 02553 3 02930 1F42 02777 1 02945 2F43 02589 2 02325 3F44 02082 4 01800 4

F5 01671 5 01528 5F51 02673 1 02716 1F52 01972 3 01934 3F53 02074 2 01888 4F54 01724 4 01500 5F55 01557 5 01962 2

up project risk management strategies for the adequate allo-cation of resources

References

[1] H M Lee ldquoApplying fuzzy set theory to evaluate the rateof aggregative risk in software developmentrdquo Fuzzy Sets andSystems vol 79 no 3 pp 323ndash336 1996

[2] Y H Kwak and J Stoddard ldquoProject risk management lessonslearned from software development environmentrdquo Technova-tion vol 24 no 11 pp 915ndash920 2004

[3] M de Oliveira Barros C M L Werner and G H TravassosldquoSupporting risks in software project managementrdquoThe Journalof Systems and Software vol 70 no 1-2 pp 21ndash35 2004

[4] S T Lu and SHYu ldquoRisk factors assessment for software devel-opment project based on fuzzy decision makingrdquo InternationalJournal of Information and Electronics Engineering vol 2 no 4pp 596ndash600 2012

[5] T-C Wang and Y-H Chen ldquoApplying fuzzy linguistic prefer-ence relations to the improvement of consistency of fuzzy AHPrdquoInformation Sciences vol 178 no 19 pp 3755ndash3765 2008

[6] E Herrera-Viedma F Herrera F Chiclana and M LuqueldquoSome issues on consistency of fuzzy preference relationsrdquoEuropean Journal of Operational Research vol 154 no 1 pp 98ndash109 2004

[7] B W Boehm ldquoSoftware risk management principles andpracticesrdquo IEEE Software vol 8 no 1 pp 32ndash41 1991

[8] H M Lee and L Lin ldquoFuzzy risk presumptive evaluationin software developmentrdquo International Journal of InnovativeComputing Information and Control vol 7 no 7 pp 3881ndash38892011

[9] J Jiang and G Klein ldquoSoftware development risks to projecteffectivenessrdquo The Journal of Systems and Software vol 52 no1 pp 3ndash10 2000

[10] D X Houston G T Mackulak and J S Collofello ldquoStochasticsimulation of risk factor potential effects for software develop-ment risk managementrdquo The Journal of Systems and Softwarevol 59 no 3 pp 247ndash257 2001

[11] G Buyukozkan and D Ruan ldquoChoquet integral based aggre-gation approach to software development risk assessmentrdquoInformation Sciences vol 180 no 3 pp 441ndash451 2010

[12] X N Lu and Q G Ma ldquoRisk analysis in software developmentproject with owners and contractorsrdquo in Proceedings of the IEEEInternational Engineering Management Conference Innovationand Entrepreneurship for Sustainable Development (IEMC rsquo04)vol 2 pp 789ndash793 October 2004

[13] T L Saaty The Analytic Hierarchy Process McGraw-Hill NewYork NY USA 1980

[14] J J Buckley ldquoRanking alternatives using fuzzy numbersrdquo FuzzySets and Systems vol 15 no 1 pp 21ndash31 1985

Mathematical Problems in Engineering 9

[15] S-J Chen and C-L Hwang Fuzzy Multiple Attribute DecisionMaking-Method and Applications Springer New York NYUSA 1992

[16] T L Saaty and L G Vargas The Logic of Priorities KluwerAcademic Boston Mass USA 1982

[17] T Y Hsieh S T Lu and G H Tzeng ldquoFuzzy MCDM approachfor planning and design tenders selection in public officebuildingsrdquo International Journal of Project Management vol 22no 7 pp 573ndash584 2004

[18] S T Lu ldquoUsing the fuzzy multiple criteria decision makingapproach for risk evaluation on investment of overseas projectrdquoin Proceedings of the 9th International Conference on MachineLearning and Cybernetics (ICMLC rsquo10) vol 4 pp 2031ndash2036July 2010

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 9

[15] S-J Chen and C-L Hwang Fuzzy Multiple Attribute DecisionMaking-Method and Applications Springer New York NYUSA 1992

[16] T L Saaty and L G Vargas The Logic of Priorities KluwerAcademic Boston Mass USA 1982

[17] T Y Hsieh S T Lu and G H Tzeng ldquoFuzzy MCDM approachfor planning and design tenders selection in public officebuildingsrdquo International Journal of Project Management vol 22no 7 pp 573ndash584 2004

[18] S T Lu ldquoUsing the fuzzy multiple criteria decision makingapproach for risk evaluation on investment of overseas projectrdquoin Proceedings of the 9th International Conference on MachineLearning and Cybernetics (ICMLC rsquo10) vol 4 pp 2031ndash2036July 2010

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of