research article an integrated approach for prioritizing...

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 563723 12 pageshttpdxdoiorg1011552013563723

Research ArticleAn Integrated Approach for Prioritizing Key Factors inImproving the Service Quality of Nursing Homes

Vincent F Yu and Kuo-Jen Hu

Department of Industrial Management National Taiwan University of Science and Technology No 43 Section 4 Keelung RoadTaipei 106 Taiwan

Correspondence should be addressed to Kuo-Jen Hu d9701102mailntustedutw

Received 28 June 2013 Revised 4 November 2013 Accepted 19 November 2013

Academic Editor Hao-Chun Lu

Copyright copy 2013 V F Yu and K-J HuThis 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 looks at improving the service quality in nursing homes as well as the intricate relationships between various factorsWe use two research models herein First Interpretive Structural Modeling (ISM) establishes the criteria for the interrelationshipstructure categorized according to their driving power and dependence This methodology provides a means by which order canbe imposed on the complexity of such criteria Insights from this model can help top managers in strategic planning to improve theservice quality in nursing home care Second because ISM does not provide any weighting associated with the criteria we employthe Analytic Network Process (ANP) approach to calculate the weighted importance of the key factors and to identify those factorsimpacting the service quality of nursing home care

1 Introduction

Nursing homes are defined as long-term aged or skilled-care facilities For an aging population nursing homes play animportant role in the provision of care for elderly people InTaiwan people pay great respect to elderly family membersand so the majority of elderly people are traditionally caredfor at home The percentage of Taiwanese people over 65years old rose from approximately 7 in 1993 to 10 by2007 and is expected to increase to about 20 by 2025In the year 2000 the life expectancy for men and womenhad increased respectively to 737 and 793 years [1] Thisrapid rate of increase has drastically raised healthcare needsand demand for long-term care Since industrialization andurbanization have changed the structure of many Taiwanesefamilies placing older family members with impairments innursing homes has become a new alternative albeit not adesirable or acceptable one by many [2] However there areno active regulations to govern nursing homes and monitortheir service quality As such the service quality of nursinghomes has become a major concern both to customers andthe government with nursing homes devoting more andmore effort to improving it In view of this we identify andprioritize the key factors in improving the service quality of

nursing homes The results of this study can serve as a goodreference for nursing homes striving to improve their service

Nursing homes are defined as facilities that provideskilled nursing services to patients with chronic conditionsHome care refers to providing needed services and equip-ment to patients and families at home The importance ofgood service quality offered by nursing homes is widely rec-ognized such as good skilled nursing and good care facilitiesProviding appropriate long-term care services and good carefacilities for elderly people is important to enhance the safetyand quality of life Therefore identifying those factors thataffect care service utilization and safe facilities has becomean important concern Nursing home care quality is a multi-dimensional construct that is difficult to define and assess [3]The literature gives several definitions of quality includingldquoQuality is the degree of agreement between the reality andpreviously set criteriardquo [4] and ldquoQuality should be defined asa continuous effort by all members of an organization tomeetthe needs and expectations of the clientsrdquo [5]

According to Donabedian [4] the assessment of nursingcare encompasses three domains structure process andoutcome The structure determines the instrumentalities ofcare and their organization including facilities equipmentmanpower and financingTheprocess evaluates the quality of

2 Mathematical Problems in Engineering

the way in which care is given which involves an assessmentof the care itself and an evaluation of the activities of theprofessional nursesThe outcome refers to the appraisal of theend results of care usually specified in terms of health wel-fare patient satisfaction patient stress and so forth Withinthese three domains this paper employs the multiple criteriadecision-making (MCDM) approach to find the evaluationcriteria that influence service quality in the nursing homeindustry based on some studies in the literature [6ndash8]

The MCDM approach is a well-known branch of deci-sion making and is widely used in ranking one or morealternatives from a set of available alternatives with multipleattributes TheMCDM approach presents an effective frame-work for decisionmaking based on the evaluation of multipleconflicting criteria A number of approaches have beenproposed for solving MCDM problems such as InterpretiveStructural Modeling (ISM) and Analytical Network Process(ANP) Warfield [9] originally proposed ISM which trans-forms the relationship among the criterionmatrix into graph-ics through a two-dimensional matrix and Boolean algebraoperations Saaty [10] offered ANP as an extension of theAnalytical Hierarchy Process (AHP) as ANP adds the depen-dence and feedback relationships to AHP In practical prob-lems the internal criteria are interdependent and there is afeedback relationship between the low-stage and high-stagecriteria ANP uses a supermatrix algorithm to identify thepriority weights of the goals criteria and alternatives In thispaper we first apply ISM to analyze the interactive relation-ship among the quality care criteria We then employ ANPto calculate the weighted importance of the criteria and toidentify key criteria of care quality in order to improvenursing home quality

The remainder of this paper is organized as followsSection 2 reviews the literature with respect to models formeasuring care quality Section 3 introduces researchmetho-dologies including ISM and ANP Section 4 presents dataanalysis applying a case with the proposed approaches toidentify the key factors of care quality in order to improvenursing home quality Section 5 discusses the results and pro-vides suggestions for improving nursing home care FinallySection 6 draws the conclusions

2 Literature Review

Many research studies have recently developed quality mod-els to assess andmanage nursing home care quality Spilsburyet al [11] employed a systematic review for the relationshipbetween nursing home and nurse staffing and how this affectsquality of care for nursing home residents Owusu-Frimponget al [12] implemented qualitative and quantitative methodsto determine patientsrsquo levels of satisfaction Goodson andJang [13] presented a Bayesian network as a tool for assessingthe quality of care in nursing homes Nyman and Bricker[14] used several measures of quality of care in a regressionanalysis Monique et al [15] studied quality systems innorthwestern Europe and the USA that improve quality ofcare Nakrem et al [8] reviewed nursing sensitive indicatorsused for nursing home care across seven nations with similarelderly care (USA Australia Norway NewZealand England

Sweden and Denmark) The findings help define sensitivenursing quality indicators for nursing home care inwhich themain focuses are use development andor test of qualityRantz et al [16] presented the Observable Indicators ofNursing Home Care Quality Instrument (OIQ) to measure anursing facilityrsquos quality during a brief on-site visit to a nurs-ing home According to scholarly research on the topic ofnursing we find that the literature mainly focuses on qual-itative and quantitative methods such as systematic reviewstatistic analysis regression analysis Bayesian network anal-ysis and so forth The MCDM approach (ISM and ANP) isalmost never applied in the field of nursing home care

ISM is a multicriteria decision-making methodology andan interactive learning process whereby a set of dissimilardirectly and indirectly related elements are structured intoa completed systemic model [17] This technique transformsunclear and poorly articulated systemmodels into visible andwell-defined models ISM is an influential approach that canbe applied in various fields Vivek et al [18] resorted to ISMto establish changing emphases of the specific elements in off-shore alliancesWanga et al [19] employed ISM to summarizethe critical barriers hindering the project of energy savingsin China and to explain the interrelationships among themLuthra et al [20] identified the contextual relationship amongthe eleven barriers to implementing green supply chainmanagement in the automobile industry Govindan et al[21] used ISM for identifying and summarizing relationshipsamong specific attributes for selecting the best third-partyreverse logistics provider among the 3PRLPs

The ANP is a comparatively simple and systematic math-ematical model that can be used in the decision-making pro-cess It incorporates the influences and interactions amongthe elements of the system as perceived by the decisionmakerand groups them into clusters Some of the most recentapplications of ANP to decision-making problems have beenas follows logistics service provider [22] supplier selection[23 24] project selection [25 26] supply chain management[27] energy policy [28] product mix planning [29] andfacility location problem [30 31] Some hybrid approachesthat combine over two kinds of MCDMmethods are appliedin the field of alternative selection problems Kannan et al[32] integrated ISM and fuzzy TOPSIS for the selection ofa reverse logistics provider Lee et al [33] employed delphiISM and fuzzy ANP to analyze the relationship amongtechnology transfer knowledge management and buyersupplier relationships in the acquisition of new equipmentLin et al [34] proposed a hybrid method that combines ISMand fuzzy ANP to cope with the problem of the differentdimensionsrsquo interdependence and feedback in the vendorselection problem

According to the literature review we are finding thatthe methods of ISM and ANP are useful analytical tools forevaluating complex systems Integrating ISM and ANP canreduce the questionnairesrsquo process and copewith the problemof different dimensionsrsquo interdependence and feedback inthe selection problem Although these approaches are widelyapplied in numerous fields for research there are few studiesin the literature that apply these approaches in the relatednursing issue to investigate the relevant problems Therefore

Mathematical Problems in Engineering 3

we propose the integrated approach to present key factors inimproving the service quality of nursing homes

3 Method

This study employs two research models ISM and ANP ISMestablishes the criteria for the interrelationship structure cat-egorized according to their driving power and dependenceThis methodology provides a means by which order can beimposed on the complexity of criteria The insights gainedfrom the model can help top managers perform strategicplanning for improving service quality in nursing home careSince ISM does not give any weighting associated with thecriteria we employ ANP to calculate the importance weightsof the key factors and to identify those factors affecting theservice quality of nursing home care Subsequent sectionsdescribe the details of the proposed approaches

31 Interpretive Structural Modeling ISM converts a complexsystem into a visualized hierarchical structure It is a methodfor analyzing and solving complex problems to managedecision makingThe method can be adopted to identify andanalyze the relationships among specific variables that definea problem or an issue [35 36] and thereby establish the hier-archical structure The overall structure is portrayed througha digraph model [37 38] which is an approach adopted forstructuring details related to a problem or activity such ascomplex technical problems [33] and competitive analysis[39]

ISM starts with the identification of factors that are rele-vant to the problem or issue and afterward extends to a groupproblem-solving technique A contextual relationship is thenchosenHaving decided the factor set and contextual relationa structural self-interactionmatrix (SSIM) is developed basedon a pairwise comparison The SSIM is developed based onthe pairwise comparison of variables and can be described as

119878 =

1198901

1198902

sdot sdot sdot 119890119899

1198901

1198902

119890119898

[[[[

[

0

12058721

1205871198981

12058712

0

1199111198982

sdot sdot sdot

sdot sdot sdot

dsdot sdot sdot

1205871119899

1205872119899

0

]]]]

]

(1)

where 119890119894represents the 119894th element and 120587

119894119895is the interrela-

tionship between the 119894th and the 119895th elements Four symbolsare used to denote the type of relation that exists between twofactors 119894 and 119895 under consideration119860 factor 119895 leads to factor119894 119881 factor 119894 leads to factor 119895119883 factor 119894 leads to factor 119895 andfactor 119895 leads to factor 119894 119874 no relationship exists betweenfactor 119894 and factor 119895

The contextual relationship of ldquoleads tordquo means that onefactor leads to another Based on the relationship between twofactors a SSIM is developed via expertsrsquo comments In thisprocess the experts discuss the direction of the relationshipbetween key agile factors clarify the intent of the factorsand ensure that only the key agile factors are includedThis process is continued until all the experts agree on thedirection of the relationship

After a SSIM is developed the binary rules are used toobtain the initial reachability matrix 119878 The substitution of 1rsquosand 0rsquos is done as follows

(1) If the (119894 119895) entry in the SSIM is119881 then the (119894 119895) entryin the reachability matrix becomes 1 and the (119895 119894)entry becomes 0


(3) If the (119894 119895) entry in the SSIM is119883 then the (119894 119895) entryand the (119895 119894) entry both become 1

(4) If the (119894 119895) entry in the SSIM is 0 then both the (119894 119895)entry and the (119895 119894) entry in the reachability matrixbecome 0

The reachability matrix is then established by

119872 = 119878 + 119868

119872119877= 119872119896= 119872119896+1

119896 gt 1

(2)

where 119868 is the identitymatrix 119896 denotes the powers119872119877is the

reachability matrix and 119872119896 denotes the stable reachability

matrix Subsequently the stable reachability set 119877(119905119894) and the

priority set 119860(119905119894) can be calculated based on (3) and (4)

respectively The former includes the element of 119890119894for all

reachable criteria whereas the latter includes all criteria ofthe reachable elements of 119890

119894 Consider

119877 (119905119894) = 119890

119894| 1205871198981198991015840 = 1 (3)

119860 (119905119894) = 119890

119894| 1205871198981015840119899= 1 (4)

We can determine the hierarchy and relationships amongcriteria using (3) and (4) Note that the reachability matrix isunder the operators of Boolean multiplication and additionFrom the final reachability matrix the reachability set 119877(119905

119894)

the antecedent set 119860(119905119894) and the intersection set 119877(119905

119894) cap 119860(119905

119894)

for each factor can be found Once the top-level factors arefound they should be separated fromother factors After thatthe next level of factors is identified by the same processes

Let criterion 119894 consist of four criteria 1198901 1198902 1198903 and 119890

4 The

values of the adjacency matrix 119878 between the criteria givenby evaluator119872 can be represented as belowWe add the adja-cency matrix to the identity matrix to form a tentative reach-ability matrix119872 at 119896 = 1 as follows

119878 =

1198901

1198902

1198903

1198904

1198901

1198902

1198903

1198904

[[[

[

0

1

1

0

1

0

1

0

0

0

0

0

0

1

0

0

]]]

]

119872 = 119878 + 119868 =

1198901

1198902

1198903

1198904

1198901

1198902

1198903

1198904

[[[

[

1

1

1

0

1

1

1

0

0

0

1

0

0

1

0

1

]]]

]

(5)


Table 1 Reachability of the criteria

119890119899

119877 (119905119894) 119860 (119905

119894) 119877 (119905

119894) cap 119860 (119905

119894) Level

1 1 2 4 1 2 3 1 2 22 1 2 4 1 2 3 1 2 23 1 2 3 4 3 3 34 4 1 2 3 4 4 1

We calculate the reachability matrix under the operatorsof the Booleanmultiplication and addition law (ie 1times1 = 11 times 0 = 0 times 1 = 0 1 + 1 = 1 1 + 0 = 1 + 0 = 1 and 0 + 0 = 0)Consider

119872 = (119878 + 119868)2=

1198901

1198902

1198903

1198904

1198901

1198902

1198903

1198904

[[[

[

1

1

1

0

1

1

1

0

0

0

1

0

1lowast

1

1lowast

1

]]]

]

(6)

where the asterisk 119896 indicates the derivative relation thatdoes not emerge in the original relation matrix (ie 119878 + 119868)According to 119877(119905

119894) cap 119860(119905

119894) we determine that the top-level

criterion is criterion 1198904in Table 1 We now can delete the row

and column corresponding to criterion 1198904from matrix 119872

Repeating the above step the second level is determined next

32 Analytic Network Process ANP is the general form of theanalytic hierarchy process [10 40] It is used inmultiple crite-ria decisionmaking to release the restriction of a hierarchicalstructure that integrates linkages and feedbacks into thedecision system in order to evaluate the overall cumulativeimportance of all indicators within an evaluation modelANP is able to include interdependent relationships amongits elements by capturing the composite weights throughthe development of a supermatrix The principal concept ofANP is parallel to the Markov chain process with the relativeimportance weights adjusted by forming a supermatrix fromeigenvectors of these weights The supermatrix is actually apartitioned matrix where each matrix segment expresses arelationship between two clusters in a system [41] Assumethat a system has 119870 clusters or components Component119901 denoted by 119862

119901 119901 = 1 119870 has 119899

119901elements denoted

by 1198901199011

1198901199012

119890119901119899119901

We formulate a standard form of asupermatrix as follows

119882 =

1198621

1198622


11989011 11989012 119890

11198991

11989021 11989022 119890

21198992

sdot sdot sdot 1198901198701 1198901198702 119890

119870119899119870

1198621

11989011

11989012

11989011198991

1198622

11989021

11989022

11989021198992

119862119870

1198901198701

1198901198702

119890119870119899119870

[[[[[[[[[[[[[[[[[[[[

[

11990811

11990821

1199081198701

11990812

11990822

1199081198702

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1199081119870

1199082119870

119908119870119870

]]]]]]]]]]]]]]]]]]]]

]

(7)

A priority vector derived from a pairwise comparison in theusual way represents the impact of a given set of elementsin a component on another element in the system When anelement has no influence on another element its influencepriority is assigned to be zero [10] As an example we givethe matrix representation of a hierarchy with three levels as

119882 = [

[

119868 0 0

11990821

0 0

0 11990832

119868

]

]

(8)

where11988221is a vector that represents the impact of the goal on

the criteria 11988232is a vector that represents the impact of the

criteria on each of the alternatives and 119868 is the identitymatrixHere 119882 is referred to as a supermatrix because its entries

are matrices For example if the criteria are interrelatedamong themselves then a network replaces the hierarchy Inaddition119882

22will be nonzero and indicates interdependence

We present this supermatrix as follows

119882 = [

[

119868 0 0

11990821

11990822

0

0 11990832

119868

]

]

(9)

Saaty and Vargas [42] captured the overall priorities ofelements according to Cesaro Summability to raise the super-matrix to limiting powers Here 119882infin = lim

119896rarrinfin(1119873)119882

119896

119895

the limit is unique and there is a column vector 119882infin for

which 119882infin

= 119908infin

times 119890119879 However if 119882 is reducible then


the multiplicity 119899119894of the principal eigenvalue has to be con-

sidered in order to obtain the limit priorities of a reduciblestochastic matrix with the principal eigenvalue being amultiple root As an illustration 119899

119894= 1 and thus we give119882infin

for a hierarchy with three levels as follows

119882infin

= lim119896rarrinfin

(

(

0 0 0

119882119896

2211988221

119882119896

220

11988232(

119896minus2

sum

ℎ=0

119882ℎ

22) 11988232(

119896minus1

sum

ℎ=0

119882ℎ

22) 119868

)

)

(10)

Now |11988222| lt 1 implies that (119882

22)119896 tends to zero as 119896 tends to

infinity and thus we have

119882infin

= (

0 0 0

0 0 0

11988232(119868 minus 119882

22)minus1

11988221

11988232(119868 minus 119882

22)minus1

119868

)

(11)

The impact of the goal for ranking the alternatives is givenby the (3 1) entry of 119882infin The matrix can always be madeprimitive by replacing all zeros by an arbitrarily small positivenumber ensuring that the matrix remains column stochastic

Limit priority values within this supermatrix indicatethe flow of influence of an individual element towards theoverall goal Since the decision alternatives are elements of anoriginal cluster of the network their limit priorities aresynonymous with their contributions to the goal and areused for ranking the alternatives being normalizedwithin thecluster

4 Case Study

We present a case study conducted in 2011 at registered nurs-ing homes in Taiwan to demonstrate the practicality of theproposed approaches The main types of nursing homes areprivate hospital-based and freestanding Private hospital-based nursing homes are owned privately The others arefreestanding that is they are owned and run by individualsor companies Some experts were selected from these nursinghomes to form a committee for conducting our researchsurvey With a comprehensive literature review [6ndash8 15]and consultations with the committee we determine fourdimensions Patientrsquos Care of Life (119863

1) Nursing Staff (119863

2)

Home Care Environment (1198633) and Home Care Facilities

(1198634) Under each of the four dimensions there are several

factors with Table 2 showing a candidate list of 20 factors

41 Analyzing Care Quality by ISM ISM is an interactivelearning process A set of different and directly related vari-ables affecting the system under consideration is structuredinto a comprehensive systemic model The beauty of the ISMmodel is that it portrays the structure of a complex issuefor the problem under study The ISM method in the firststage inquires expertsrsquo opinions in developing the contextualrelationship among all factors In this study pairwise com-parisons are formed by the experts

Table 2 Dimensions and factors affecting nursing home quality

Dimensions Factors

Patientrsquos Care ofLife (119863

1)

Emergency Processing Speed (F1)Rapid and Appropriate Referral (F2)Medical andTherapeutic Care (F3)Pain Management (F4)Clinical Care (F5)

Nursing Staff(1198632)

Good Service Attitude (F6)Specialized Nursing Care (F7)Staff Complement (F8)Physician Involvement (F9)Sufficient and Competent Staff (F10)

Home CareEnvironment(1198633)

Space Requirements (F11)Hygiene and Infection Control (F12)Public Area Clean and Neat (F13)Health and Safety Management (F14)Good Living Environment (F15)

Home CareFacilities (119863

4)

Appropriate Bed Distribution (F16)Enough Illumination (F17)Bathroom and Toilet Facilities (F18)Medical Instrument (F19)Monitoring Information System (F20)

After pairwise comparisons we construct the structuralself-interaction matrix (SSIM) as shown in Table 3 We thentransform the SSIM into a binary matrix called the initialreachability matrix by substituting 119881 119860 119883 and 119874 by 1 and0 as per the case The transforming rules for the substitutionof 1rsquos and 0rsquos are shown in Section 31 The initial reachabilitymatrix in Table 4 is finished based on Table 3The final reach-ability matrix in Table 5 can be obtained from transitivitychecks that have been carried out to extract a consistentmodel from the set of factors as enumerated in the ISMapproach in Section 31 Partitioning the reachability matrixis continuously constructed by assessing the reachability andantecedent sets for each factor The reachability set encom-passes the factors themselves and the other factors that itcan reachThe antecedent set contains the factors themselvesand the other factors that may help in achieving them Theintersection of these sets is derived for all factors If the factorsfall into the reachability set the same as the intersection setsthen the factors can be given the first-level factors in theISM hierarchy which does not help achieve any other factorsabove their own level The same process is repeated to findthe next level of factors In the present case Table 6 showsthe factors along with their reachability set antecedent setintersection set and levels

After the reachability matrix is partitioned we constructthe driver power and dependence for each factor The driverpower and dependence in this study are used to identifyand to analyze the factors Summations of the row show thedriver power of the factor and summations of the columnindicate dependence in Table 5mdashfor example factor 7 has


Table 3 Structural self-interaction matrix (SSIM)

Factors 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 11 O O O O O O X O O O A A O A O O O O V mdash2 O O O O O O V O V O O O O O O V O O mdash3 O O O O O O V O V O O O O O O V V mdash4 O O O O O O V O O O O A O O O O mdash5 O O O O O O V O V O O X O X O mdash6 O O O O O O O O O O O O O O mdash7 O O O O O O O O V O O O O mdash8 O O O O O O O O O O A O mdash9 O O O O O O V O V O O mdash10 O O O O O O O O O O mdash11 O O V O O O O O O mdash12 O O O O O A X O mdash13 O O O O O X O mdash14 O O O O O O mdash15 O O X X O mdash16 O O O O mdash17 O O O mdash18 O O mdash19 O mdash20 mdash

Table 4 Initial reachability matrix

Factors 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 201 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 02 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 03 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 04 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 05 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 07 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 08 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 09 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 010 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 011 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 012 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 013 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 014 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 015 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 016 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 017 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 018 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 019 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 020 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

a driving power of 8 and a dependence of 15The driver powerand dependence can be grouped into four clusters as shownin Figure 1 The first cluster encompasses the autonomousfactors that have weak driver power and weak dependenceAll factors in this area express a relative disconnection fromthe system in which they have only a few links and may

be strong The second cluster consists of the dependentfactors that have weak driver power but strong dependenceThe third cluster includes factors that have strong driverpower and strong dependence These factors are unstable Itis easy to influence the others when taking any action onthese factors and there is also a feedback on themselves


Table 5 Final reachability matrix

Factors 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Driver power1 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 82 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 83 1 1 1 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 94 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 85 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 86 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 17 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 88 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 19 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 810 1 1 0 1 1 0 1 1 1 1 0 1 0 1 0 0 0 0 0 0 1011 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 0 0 1312 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 813 1 1 0 1 1 0 1 0 1 0 0 1 1 1 1 0 1 1 0 0 1214 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 815 1 1 0 1 1 0 1 0 1 0 0 1 1 1 1 0 1 1 0 0 1216 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 117 1 1 0 1 1 0 1 0 1 0 0 1 1 1 1 0 1 1 0 0 1218 1 1 0 1 1 0 1 0 1 0 0 1 1 1 1 0 1 1 0 0 1219 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 120 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1Dependence power 15 15 1 15 15 1 15 2 15 1 1 15 5 15 5 1 5 5 1 1

Table 6 Level partitions for factorsrsquo iteration

Factors Reachability set Antecedent set Intersection set Level1 1 2 4 5 7 9 12 14 1 2 3 4 5 7 9 10 11 12 13 14 15 17 18 1 2 4 5 7 9 12 14 II2 1 2 4 5 7 9 12 14 1 2 3 4 5 7 9 10 11 12 13 14 15 17 18 1 2 4 5 7 9 12 14 II3 1 2 3 4 5 7 9 12 14 3 3 III4 1 2 4 5 7 9 12 14 1 2 3 4 5 7 9 10 11 12 13 14 15 17 18 1 2 4 5 7 9 12 14 II5 1 2 4 5 7 9 12 14 1 2 3 4 5 7 9 10 11 12 13 14 15 17 18 1 2 4 5 7 9 12 14 II6 6 6 6 I7 1 2 4 5 7 9 12 14 1 2 3 4 5 7 9 10 11 12 13 14 15 17 18 1 2 4 5 7 9 12 14 II8 8 8 10 8 II9 1 2 4 5 7 9 12 14 1 2 3 4 5 7 9 10 11 12 13 14 15 17 18 1 2 4 5 7 9 12 14 II10 1 2 4 5 7 8 9 10 12 14 10 10 III11 1 2 4 5 7 9 11 12 13 14 15 17 18 11 11 V12 1 2 4 5 7 9 12 14 1 2 3 4 5 7 9 10 11 12 13 14 15 17 18 1 2 4 5 7 9 12 14 II13 1 2 4 5 7 9 12 13 14 15 17 18 11 13 15 17 18 13 15 17 18 IV14 1 2 4 5 7 9 12 14 1 2 3 4 5 7 9 10 11 12 13 14 15 17 18 1 2 4 5 7 9 12 14 II15 1 2 4 5 7 9 12 13 14 15 17 18 11 13 15 17 18 13 15 17 18 IV16 16 16 16 I17 1 2 4 5 7 9 12 13 14 15 17 18 11 13 15 17 18 13 15 17 18 IV18 1 2 4 5 7 9 12 13 14 15 17 18 11 13 15 17 18 13 15 17 18 IV19 19 19 19 I20 20 20 20 I

The fourth cluster includes the independent factors having astrong driver power but weak dependenceThe driver power-dependence matrix reveals the following results

(1) Autonomous In this case F6 (Good Service Attitude)F8 (Staff Complement) F16 (Appropriate Bed Distribution)

F19 (Medical Instrument) and F20 (Monitoring InformationSystem) are categorized as autonomous These barriers haveless influence on the overall system and in many ways canbe handled independently during the interventionThis indi-cates that these factors have few direct linkages throughoutthe system


F14F12F3 F9F7

F20

F5

F8

F4F10

F11

F2

F15

F1

F13

F19

F18F17

F16F6

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16

Driv

er p

ower

Dependence power

LinkageIndependent

Autonomous Dependent

Figure 1 Driver power and dependence power diagram

(2) DependentThe dependent factor has weak driving powerbut strong dependence Since factors in this area are the weakdrivers any action on such factors should usually wait untiltheir driving variables have been addressed No such factorsare found in the dependent factor

(3) Linkage The factors falling into this area have strongdriver power and strong dependence including F1 (Emer-gency Processing Speed) F2 (Rapid and Appropriate Refer-ral) F4 (Pain Management) F5 (Clinical Care) F7 (Spe-cialized Nursing Care) F9 (Physician Involvement) F12(Hygiene and Infection Control) and F14 (Health and SafetyManagement) These factors are unstable which means thatany action on these criteria has an effect on the others andalso a feedback effect on themselvesTherefore improving itsservice quality must be considered as a top priority

(4) IndependentWe observe that F3 (Medical andTherapeu-tic Care) F10 (Sufficient and Competent Staff) F11 (SpaceRequirements) F13 (Public Area Clean and Neat) F15 (GoodLiving Environment) F17 (Enough Illumination) and F18(Bathroom and Toilet Facilities) are in the third quadrantThese are independent factors that have a significant influ-ence on the system and drive the factors above them Becauseof their high driver power and low dependence addressingthese factors early in the intervention will help establish asolid foundation for the intervention and improve the servicequality in nursing care as it tackles the remaining factors

42 Ranking Key Factors by the ANP Method We haveapplied the ISM method to analyze all factors aiming tofacilitate the interrelationships of each factor with the otherfactors The factors can be classified into four clusters torealize the driver power and dependence of all factorsHowever even though the interrelationship of all factorscan be classified using the ISM method the importance ofthe factors is difficult to be presented by using the sameapproachTherefore we implement the ANPmethod to rankthe importance of all factors in this section

Figure 2 constructs the complete network hierarchySattyrsquos nine-point scale pairwise comparison was preparedto set up a questionnaire and five experts in nursing carefrom an anonymous nursing home in Taiwan were askedto fill out the questionnaire The consistency property of

each matrix from each expert was checked first to ensurethe consistency of judgments in the pairwise comparisonThe pairwise comparisons were entered into the (2 1) (2 2)(3 2) and (3 3) blocksrsquo super-matrix before convergence inTable 7

The results of pairwise comparisons 11988221

and 11988232

showthe priorities of dimensions and factors with respect todimensions when the interrelationship among factors wasnot considered The interrelationships among dimension(11988222) are depicted in the (2 2) block In addition the

interrelationships among factors (11988233) are developed based

on Table 5 in the (3 3) block For example column four hastwo rows to show that the value is one That means factors3 and 9 must complete a pairwise comparison to find outthe interrelationships among these factors Table 7 shows thetotal final values of119882

211198822211988232 and119882

33 For example the

priorities of the dimensions (1198631to 1198634) with respect to the

goal are 0318 0248 0252 and 0181 respectivelyWe weight the unweighted supermatrix first We then

raise the weighted supermatrix to limiting powers in orderto capture all the interactions and to obtain a convergenceoutcome After the weighted supermatrix we present thepriorities in Table 8

According to the results of Table 8 the order of impor-tance for the dimensions is Patientrsquos Care of Life (119863

1) = 03128

Nursing Staff (1198632) = 02858 Home Care Environment (119863

3) =

02383 andHomeCare Facilities (1198634) = 01632 Patientrsquos Care

of Life (1198631) is the key dimension that affects the quality of

improvement in a nursing home From the expertsrsquo viewpointand experience in nursing care Patientrsquos Care of Life is moreimportant than the other dimensions Because a patientrsquosdaily care impacts the health and safety of the people wholive in nursing homes the patients themselves as well as theirfamily look for good care of life in a nursing home

Looking at the results of the global weights the topten priorities of factors are Rapid and Appropriate Referral(F2) gt Specialized Nursing Care (F7) gt Pain Management(F4) gt Health and Safety Management (F14) gt EmergencyProcessing Speed (F1) gt Good Service Attitude (F6) gt

Sufficient andCompetent Staff (F10)gtPhysician Involvement(F9) gt Hygiene and Infection Control (F12) gt Public AreaClean and Neat (F13) In order to effectively improve thequality of nursing care those quality elements with a higherglobal weight should receive greater emphasis regardingimprovement

5 Discussion

As current generations get older and enter retirement thethought of entering a nursing home can leave many withunsettled mixed emotions News stories frequently highlightpoor treatment in senior living homes Thus it is importantfor nursing homes to focus more on the treatment ofresidents With proper customer service a nursing home canbe a pleasant place for all residents In this study we findsome factors that improve service quality which must beconsidered as a top priority

Rapid and Appropriate Referral (00902) and SpecializedNursing Care (00769) are the respective first and second


Goal

F20F19F18F17F16F5F4F3F2F1 F10F9F8F7F6 F15F14F13F12F11

W22

W21

W32

W33

D1 D2 D3 D4

Figure 2 The ANP hierarchy

priorities that require improvement Older people in nursinghomes are vulnerable to conditions causing disability InTaiwan at least 70 of older people suffer from one or morechronic illnesses such as cancer cerebral vascular diseasehypertension heart disease diabetes and arthritis [43] Thedemand for Rapid and Appropriate Referral and SpecializedNursing Care for disabled and chronically ill older people isvery important in Taiwan Therefore we suggest increasingthe number of professional nursing staffs engaged in nursingcare and constructing a nursing care team for monitoringolder people who need medical treatment as well as directingpatients to a medical specialist

We provide some aspects for improving Pain Manage-ment (00765) A nursing home may designate responsibilityand accountability to specific staff positions for the screeningof pain at admission and they can do so periodically thereafteras part of their routine interaction with residents They canalso educate all the staff members about pain symptoms inelderly people to address preexisting attitudes about suchpain or knowledge deficits about pain manifestations incognitively impaired individuals They can use standardizedevaluation tools including pain-rating scales to evaluateresidentsrsquo complaints of pain found during screening and totrain nursing staff about effective communication with physi-cians about pain management

Health and Safety Management (00710) is also a keyaspect of nursing care We suggest concrete efforts be madeto establish a systematic standardized health and safetyman-agement system and mechanism To achieve this a nursinghome has to set up its own health and safety managementsystem to ensure the safety of all patients and nursing staffsthrough continuous improvement in the management sys-tem This system covers education training consultationprevention and risk monitoring of serious diseases forpatients nursing staffs and their families

Emergency Processing Speed (00666) should beimproved so as to enhance the quality of nursing care Wesuggest that a nursing home develop a workable emergencyevacuation plan This plan has to provide guidance in the

development of an evacuation plan containing detailedinformation instructions and procedures that can beexecuted under any emergency situation necessitating eithera full or partial evacuation of the nursing home or assistedcare facility This plan must incorporate staff roles and res-ponsibilities essential to this process Staff must be educatedin their role These factors indicate that nursing homeresidents are concerned about their health and safety If anursing home can make residents feel confident regarding itsability to deal with emergencies and health and safety thenresidentsrsquo satisfaction will increase

6 Conclusions

This research has employed the ISM and ANP methods toprioritize key factors for improving the service quality ofnursing homes in Taiwanrsquos nursing home industry First weuse ISM to systematically explore the causal relationshipsamong various factors Second we implement ANP to iden-tify the importance weights of the factors in improving theservice quality of nursing homes The findings show thatthe ISM technique can only help to prioritize the strategicissues during an assessment of the quality of nursing carein the sense that it explores the influences and dependencesbetween factors that affect the quality of nursing care andclassifies them into independent linkage dependent andautonomous clusters It appears that ISM does not fullypresent the ability to depict what the key factors are HoweverISM can assist ANP in generating a quantifiable discussionwhich appears more reasonable when presenting the identi-fication of the key factors for improving the service quality ofnursing homes

The use of the ISM-ANP model in decision makingis extremely useful because both visualized analysis andquantified priorities can be obtained to assist managementin decision making According to the results herein we areable to determine not only the rank order of all factors thataffect the quality improvement of nursing care but also theassessment status of all possible causal relationships among


Table7Superm

atrix

before

convergence

Goal

Dim

ensio

nsFactors

G1198631

1198632

1198633

1198634

F1F2

F3F4

F5F6

F7F8

F9F10

F11

F12

F13

F14

F15

F16

F17

F18

F19

F20

Goal

G

Dim

ensio

ns

1198631

0318

00323

0261

0403

1198632

0248

0624

00345

0239

1198633

0252

0334

0255

00358

1198634

0181

0041

0422

0394

0F1

0216

00

00

00

00

00

00

00095

00

00

00

F20289

00

00

0284

00

00

00

0051

00065

00

00

00

F30136

00

0064

50367

00

00

00

0118

00145

00

00

00

F40246

00

00

00

00

00

00

00242

00

00

00

F50112

00

00

00

00

00

00148

00222

00

00

00

F60237

00

00

00

00

00

00

00

00

00

00

F70267

021

00

00189

00

00

00

0159

00

00

00

00

F80126

00

00

00

00

00

00

00

00

00

00

F90165

029

00

0355

0159

00

00

00

0207

00159

00

00

00

Factors

F10

0204

03590

00

00

00

00

00

00

00

00

00

0F11

0193

00

00

00

00

00

00

00

00

0453

00

F12

0205

00

00

00

00

00

00

00073

00

00

00

F13

0197

00

00

00

00

00

00

00

032

00

00

0F14

0299

0141

00

00

00

00

00

0124

00

00

00

00

F15

0107

00

00

00

00

00

00192

00

00

00547

00

F16

0287

00

00

00

00

00

00

00

00

00

00

F17

0242

00

00

00

00

00

00

00

0285

00

00

0F18

0262

00

00

00

00

00

00

00

0396

00

00

0F19

0020

00

00

00

00

00

00

00

00

00

00

F20

0189

00

00

00

00

00

00

00

00

00

00


Table 8 Priorities of dimensions and factors

Dimensions Local weight Factors Local weight Global weight Priorities

Patientrsquos Care of Life (1198631) 03128

Emergency Processing Speed (F1) 02130 00666 5Rapid and Appropriate Referral (F2) 02885 00902 1Medical andTherapeutic Care (F3) 01416 00443 13

Pain Management (F4) 02446 00765 3Clinical Care (F5) 01123 00351 17

Nursing Staff (1198632) 02858

Good Service Attitude (F6) 02324 00664 6Specialized Nursing Care (F7) 02691 00769 2

Staff Complement (F8) 01237 00354 16Physician Involvement (F9) 01711 00489 8

Sufficient and Competent Staff (F10) 02037 00582 7

Home Care Environment (1198633) 02383

Space Requirements (F11) 01938 00462 12Hygiene and Infection Control (F12) 02023 00482 9Public Area Clean and Neat (F13) 01962 00468 10

Health and Safety Management (F14) 02980 00710 4Good Living Environment (F15) 01097 00261 19

Home Care Facilities (1198634) 01632

Appropriate Bed Distribution (F16) 02843 00464 11Enough Illumination (F17) 02430 00397 15

Bathroom and Toilet Facilities (F18) 02653 00433 14Medical Instrument (F19) 00201 00033 20

Monitoring Information System (F20) 01873 00306 18

all factors Significantly the proposedmethodprovides objec-tive information to identify and evaluate the key factors forimproving the quality of nursing care

There are two noteworthy limitations to this studygeneralizability and expertsrsquo judgments First the general-izability of these research findings is limited because theyare generated from a specific nursing home industry Theresearch design was not intended to produce results thataccount for or predict the decision-making problem in allindustries To apply the proposed methodology to otherindustries an adjustment to the dimensions and factors maybe needed Second in the theory of multiple criteria decisionmaking real-world decision-making problems are usuallycomplex and ill-structured Each decision making is basedon a decision makerrsquos preferences experiences judgmentsand organizational policy Therefore one decision makerrsquosjudgment is expected to differ from anotherrsquos because theresults reflect only the opinions of the experts who tookpart in this research Therefore invited experts should havesufficiently wide experience in the research industry and betruly representative in providing data that could be appliedto top management in the researchrsquos targeted industry

Acknowledgments

The authors thank the editors and referees for their helpfulcomments and suggestions This work was partially sup-ported by the National Science Council of Taiwan underGrant NSC 102-2221-E-011-082-MY3 This support is grate-fully acknowledged

References

[1] S-C Wu A White K Cash and S Foster ldquoNursing home carefor older people in Taiwan a process of forced choicerdquo Journalof Clinical Nursing vol 18 no 14 pp 1986ndash1993 2009

[2] H-F Kao and A K Stuifbergen ldquoFamily experiences related tothe decision to institutionalize an elderly member in Taiwan anexploratory studyrdquo Social Science amp Medicine vol 49 no 8 pp1115ndash1123 1999

[3] M Gerteis J S Gerteis D Newman and C Koepke ldquoTestingconsumersrsquo comprehension of quality measures using alterna-tive reporting formatsrdquo Health Care Financing Review vol 28no 3 pp 31ndash45 2007

[4] A Donabedian The Definition of Quality and Approaches toIts Assessment vol 1 of Explorations in Quality Assessment andMonitoring Health Administration Press Chicago Ill USA1980

[5] G Laffel and D Blumenthal ldquoThe case for using industrialquality management science in health care organizationsrdquoJournal of the American Medical Association vol 262 no 20pp 2869ndash2873 1989

[6] C-L Chang ldquoApplication of quality function deploymentlaunches to enhancing nursing home service qualityrdquo TotalQuality Management and Business Excellence vol 17 no 3 pp287ndash302 2006

[7] L-L Lee NHsu and S-C Chang ldquoAn evaluation of the qualityof nursing care in orthopaedic unitsrdquo Journal of OrthopaedicNursing vol 11 no 3-4 pp 160ndash168 2007

[8] S Nakrem A G Vinsnes G E Harkless B Paulsen and ASeim ldquoNursing sensitive quality indicators for nursing homecare international review of literature policy and practicerdquo


International Journal of Nursing Studies vol 46 no 6 pp 848ndash857 2009

[9] J N Warfield ldquoToward interpretation of complex structuralmodelingrdquo IEEETransactions on SystemsMan andCyberneticsvol 4 no 5 pp 405ndash417 1974

[10] T L SaatyDecisionMaking with Dependence and FeedbackTheAnalytical Network Process vol 9 of Analytic Hierarchy ProcessRWS Publications Pittsburgh Pa USA 1996

[11] K Spilsbury C Hewitt L Stirk and C Bowman ldquoThe rela-tionship between nurse staffing and quality of care in nursinghomes a systematic reviewrdquo International Journal of NursingStudies vol 48 no 6 pp 732ndash750 2011

[12] N Owusu-Frimpong S Nwankwo and B Dason ldquoMeasuringservice quality and patient satisfaction with access to publicand private healthcare deliveryrdquo International Journal of PublicSector Management vol 23 no 3 pp 203ndash220 2010

[13] J Goodson and W Jang ldquoAssessing nursing home care qualitythrough Bayesian networksrdquo Health Care Management Sciencevol 11 no 4 pp 382ndash392 2008

[14] J A Nyman and D L Bricker ldquoProfit incentives and technicalefficiency in the production of nursing home carerdquo Review ofEconomics amp Statistics vol 71 no 4 pp 586ndash594 1989

[15] F M T Monique M Du J van Haastregt and P H H JanldquoMonitoring quality of care in nursing homes and makinginformation available for the general public state of the artrdquoPatient Education and Counseling vol 78 no 3 pp 288ndash2962010

[16] M J Rantz A Jensdottir I Hjaltadottir et al ldquoInternationalfield test results of the observable indicators of nursing homecare quality instrumentrdquo International Nursing Review vol 49no 4 pp 234ndash242 2002

[17] E Fontela ldquoThe future societal bill methodological alterna-tivesrdquo Futures vol 35 no 1 pp 25ndash36 2003

[18] S D Vivek D K Banwet and R Shankar ldquoAnalysis ofinteractions among core transaction and relationship-specificinvestments the case of offshoringrdquo Journal of OperationsManagement vol 26 no 2 pp 180ndash197 2008

[19] G H Wang Y X Wang and T Zhao ldquoAnalysis of interactionsamong the barriers to energy saving in Chinardquo Energy Policyvol 36 no 6 pp 1879ndash1889 2008

[20] S Luthra V Kumar S Kumar and A Haleem ldquoBarriersto implement green supply chain management in automobileindustry using interpretive structural modeling technique-an Indian perspectiverdquo Journal of Industrial Engineering andManagement vol 4 no 2 pp 231ndash257 2011

[21] K Govindan M Palaniappan Q Zhu and D Kannan ldquoAnal-ysis of third party reverse logistics provider using interpretivestructural modelingrdquo International Journal of Production Eco-nomics vol 140 no 1 pp 204ndash211 2012

[22] S Jharkharia and R Shankar ldquoSelection of logistics ser-vice provider an analytic network process (ANP) approachrdquoOmega vol 35 no 3 pp 274ndash289 2007

[23] S C Ting and D I Cho ldquoAn integrated approach for supplierselection and purchasing decisionsrdquo Supply ChainManagementvol 13 no 2 pp 116ndash127 2008

[24] A H I Lee ldquoA fuzzy supplier selection model with theconsideration of benefits opportunities costs and risksrdquo ExpertSystems with Applications vol 36 no 2 pp 2879ndash2893 2009

[25] L M Meade and A Presley ldquoRampD project selection using theanalytic network processrdquo IEEE Transactions on EngineeringManagement vol 49 no 1 pp 59ndash66 2002

[26] E W L Cheng and H Li ldquoAnalytic network process appliedto project selectionrdquo Journal of Construction Engineering andManagement vol 131 no 4 pp 459ndash466 2005

[27] A Agarwal R Shankar and M K Tiwari ldquoModeling themetrics of lean agile and leagile supply chain an ANP-basedapproachrdquo European Journal of Operational Research vol 173no 1 pp 211ndash225 2006

[28] B Haktanırlar ldquoDetermination of the appropriate energy policyfor Turkeyrdquo Energy vol 30 no 7 pp 1146ndash1161 2005

[29] S Chung A H I Lee and W L Pearn ldquoAnalytic net-work process (ANP) approach for product mix planning insemiconductor fabricatorrdquo International Journal of ProductionEconomics vol 96 no 1 pp 15ndash36 2005

[30] F Y Partovi ldquoAn analytic model for locating facilities strategi-callyrdquo Omega vol 34 no 1 pp 41ndash55 2006

[31] J Sarkis and R P Sundarraj ldquoHub location at digital equipmentcorporation a comprehensive analysis of qualitative and quan-titative factorsrdquo European Journal of Operational Research vol137 no 2 pp 336ndash347 2002

[32] G Kannan S Pokharel and P S Kumar ldquoA hybrid approachusing ISM and fuzzy TOPSIS for the selection of reverselogistics providerrdquo Resources Conservation and Recycling vol54 no 1 pp 28ndash36 2009

[33] A H I Lee W-M Wang and S-B Lin ldquoAn evaluation frame-work for technology transfer of new equipment in high technol-ogy industryrdquo Technological Forecasting and Social Change vol77 no 1 pp 135ndash150 2010

[34] Y-T Lin C-L Lin H-C Yu and G-H Tzeng ldquoA novel hybridMCDMapproach for outsourcing vendor selection a case studyfor a semiconductor company in Taiwanrdquo Expert Systems withApplications vol 37 no 7 pp 4796ndash4804 2010

[35] A P Sage Interpretive Structural Modeling Methodology forLarge-Scale Systems McGraw Hill New York NY USA 1977

[36] J NWarfield Societal Systems Planning Policy and ComplexitySystems and Controls for Financial Managemen John Wileyand Sons New York NY USA 1976

[37] A Mandal and S G Deshmukh ldquoVendor selection usinginterpretive structuralmodeling (ISM)rdquo International Journal ofOperations and Production Management vol 14 no 6 pp 52ndash59 1994

[38] V C Pandey G Suresh and S Ravi ldquoAn interpretive structuralmodeling of enabler variables for integration in supply chainmanagementrdquo Productivity vol 46 no 1 pp 93ndash108 2005

[39] K S Rajesh K G Suresh and S G Deshmukh ldquoInterpretivestructural modelling of factors for improving competitivenessof SMEsrdquo International Journal of Productivity and QualityManagement vol 2 no 4 pp 423ndash440 2007

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

[41] L M Meade and J Sarkis ldquoAnalyzing organizational projectalternatives for agile manufacturing processes an analyti-cal network approachrdquo International Journal of ProductionResearch vol 37 no 2 pp 241ndash261 1999

[42] T L Saaty and L G Vargas ldquoDiagnosis with dependentsymptoms bayes theorem and the analytic hierarchy processrdquoOperations Research vol 46 no 4 pp 491ndash502 1998

[43] I-C Li and T J-C Yin ldquoCare needs of residents in community-based long-term care facilities in Taiwanrdquo Journal of ClinicalNursing vol 14 no 6 pp 711ndash718 2005

Submit your manuscripts athttpwwwhindawicom

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Stochastic AnalysisInternational Journal of


the way in which care is given which involves an assessmentof the care itself and an evaluation of the activities of theprofessional nursesThe outcome refers to the appraisal of theend results of care usually specified in terms of health wel-fare patient satisfaction patient stress and so forth Withinthese three domains this paper employs the multiple criteriadecision-making (MCDM) approach to find the evaluationcriteria that influence service quality in the nursing homeindustry based on some studies in the literature [6ndash8]

The MCDM approach is a well-known branch of deci-sion making and is widely used in ranking one or morealternatives from a set of available alternatives with multipleattributes TheMCDM approach presents an effective frame-work for decisionmaking based on the evaluation of multipleconflicting criteria A number of approaches have beenproposed for solving MCDM problems such as InterpretiveStructural Modeling (ISM) and Analytical Network Process(ANP) Warfield [9] originally proposed ISM which trans-forms the relationship among the criterionmatrix into graph-ics through a two-dimensional matrix and Boolean algebraoperations Saaty [10] offered ANP as an extension of theAnalytical Hierarchy Process (AHP) as ANP adds the depen-dence and feedback relationships to AHP In practical prob-lems the internal criteria are interdependent and there is afeedback relationship between the low-stage and high-stagecriteria ANP uses a supermatrix algorithm to identify thepriority weights of the goals criteria and alternatives In thispaper we first apply ISM to analyze the interactive relation-ship among the quality care criteria We then employ ANPto calculate the weighted importance of the criteria and toidentify key criteria of care quality in order to improvenursing home quality

The remainder of this paper is organized as followsSection 2 reviews the literature with respect to models formeasuring care quality Section 3 introduces researchmetho-dologies including ISM and ANP Section 4 presents dataanalysis applying a case with the proposed approaches toidentify the key factors of care quality in order to improvenursing home quality Section 5 discusses the results and pro-vides suggestions for improving nursing home care FinallySection 6 draws the conclusions

2 Literature Review

Many research studies have recently developed quality mod-els to assess andmanage nursing home care quality Spilsburyet al [11] employed a systematic review for the relationshipbetween nursing home and nurse staffing and how this affectsquality of care for nursing home residents Owusu-Frimponget al [12] implemented qualitative and quantitative methodsto determine patientsrsquo levels of satisfaction Goodson andJang [13] presented a Bayesian network as a tool for assessingthe quality of care in nursing homes Nyman and Bricker[14] used several measures of quality of care in a regressionanalysis Monique et al [15] studied quality systems innorthwestern Europe and the USA that improve quality ofcare Nakrem et al [8] reviewed nursing sensitive indicatorsused for nursing home care across seven nations with similarelderly care (USA Australia Norway NewZealand England

Sweden and Denmark) The findings help define sensitivenursing quality indicators for nursing home care inwhich themain focuses are use development andor test of qualityRantz et al [16] presented the Observable Indicators ofNursing Home Care Quality Instrument (OIQ) to measure anursing facilityrsquos quality during a brief on-site visit to a nurs-ing home According to scholarly research on the topic ofnursing we find that the literature mainly focuses on qual-itative and quantitative methods such as systematic reviewstatistic analysis regression analysis Bayesian network anal-ysis and so forth The MCDM approach (ISM and ANP) isalmost never applied in the field of nursing home care

ISM is a multicriteria decision-making methodology andan interactive learning process whereby a set of dissimilardirectly and indirectly related elements are structured intoa completed systemic model [17] This technique transformsunclear and poorly articulated systemmodels into visible andwell-defined models ISM is an influential approach that canbe applied in various fields Vivek et al [18] resorted to ISMto establish changing emphases of the specific elements in off-shore alliancesWanga et al [19] employed ISM to summarizethe critical barriers hindering the project of energy savingsin China and to explain the interrelationships among themLuthra et al [20] identified the contextual relationship amongthe eleven barriers to implementing green supply chainmanagement in the automobile industry Govindan et al[21] used ISM for identifying and summarizing relationshipsamong specific attributes for selecting the best third-partyreverse logistics provider among the 3PRLPs

The ANP is a comparatively simple and systematic math-ematical model that can be used in the decision-making pro-cess It incorporates the influences and interactions amongthe elements of the system as perceived by the decisionmakerand groups them into clusters Some of the most recentapplications of ANP to decision-making problems have beenas follows logistics service provider [22] supplier selection[23 24] project selection [25 26] supply chain management[27] energy policy [28] product mix planning [29] andfacility location problem [30 31] Some hybrid approachesthat combine over two kinds of MCDMmethods are appliedin the field of alternative selection problems Kannan et al[32] integrated ISM and fuzzy TOPSIS for the selection ofa reverse logistics provider Lee et al [33] employed delphiISM and fuzzy ANP to analyze the relationship amongtechnology transfer knowledge management and buyersupplier relationships in the acquisition of new equipmentLin et al [34] proposed a hybrid method that combines ISMand fuzzy ANP to cope with the problem of the differentdimensionsrsquo interdependence and feedback in the vendorselection problem

According to the literature review we are finding thatthe methods of ISM and ANP are useful analytical tools forevaluating complex systems Integrating ISM and ANP canreduce the questionnairesrsquo process and copewith the problemof different dimensionsrsquo interdependence and feedback inthe selection problem Although these approaches are widelyapplied in numerous fields for research there are few studiesin the literature that apply these approaches in the relatednursing issue to investigate the relevant problems Therefore



3 Method




119878 =

1198901

1198902


1198901

1198902

119890119898

[[[[

[

0

12058721

1205871198981

12058712

0

1199111198982

sdot sdot sdot

sdot sdot sdot

dsdot sdot sdot

1205871119899

1205872119899

0

]]]]

]

(1)











119872 = 119878 + 119868

119872119877= 119872119896= 119872119896+1

119896 gt 1

(2)







119894 Consider

119877 (119905119894) = 119890

119894| 1205871198981198991015840 = 1 (3)

119860 (119905119894) = 119890

119894| 1205871198981015840119899= 1 (4)


119894)


119894) cap 119860(119905

119894)



4 The


119878 =

1198901

1198902

1198903

1198904

1198901

1198902

1198903

1198904

[[[

[

0

1

1

0

1

0

1

0

0

0

0

0

0

1

0

0

]]]

]

119872 = 119878 + 119868 =

1198901

1198902

1198903

1198904

1198901

1198902

1198903

1198904

[[[

[

1

1

1

0

1

1

1

0

0

0

1

0

0

1

0

1

]]]

]

(5)



119890119899

119877 (119905119894) 119860 (119905

119894) 119877 (119905

119894) cap 119860 (119905

119894) Level

1 1 2 4 1 2 3 1 2 22 1 2 4 1 2 3 1 2 23 1 2 3 4 3 3 34 4 1 2 3 4 4 1


119872 = (119878 + 119868)2=

1198901

1198902

1198903

1198904

1198901

1198902

1198903

1198904

[[[

[

1

1

1

0

1

1

1

0

0

0

1

0

1lowast

1

1lowast

1

]]]

]

(6)


119894) cap 119860(119905






119901 119901 = 1 119870 has 119899


by 1198901199011

1198901199012

119890119901119899119901


119882 =

1198621

1198622


11989011 11989012 119890

11198991

11989021 11989022 119890

21198992

sdot sdot sdot 1198901198701 1198901198702 119890

119870119899119870

1198621

11989011

11989012

11989011198991

1198622

11989021

11989022

11989021198992

119862119870

1198901198701

1198901198702

119890119870119899119870

[[[[[[[[[[[[[[[[[[[[

[

11990811

11990821

1199081198701

11990812

11990822

1199081198702

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1199081119870

1199082119870

119908119870119870

]]]]]]]]]]]]]]]]]]]]

]

(7)


119882 = [

[

119868 0 0

11990821

0 0

0 11990832

119868

]

]

(8)







119882 = [

[

119868 0 0

11990821

11990822

0

0 11990832

119868

]

]

(9)


119896rarrinfin(1119873)119882

119896

119895


which 119882infin

= 119908infin







119882infin


(

(

0 0 0

119882119896

2211988221

119882119896

220

11988232(

119896minus2

sum

ℎ=0

119882ℎ

22) 11988232(

119896minus1

sum

ℎ=0

119882ℎ

22) 119868

)

)

(10)




119882infin

= (

0 0 0

0 0 0

11988232(119868 minus 119882

22)minus1

11988221

11988232(119868 minus 119882

22)minus1

119868

)

(11)



4 Case Study



2)






Dimensions Factors


1)







4)








Factors 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 201 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 02 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 03 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 04 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 05 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 07 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 08 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 09 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 010 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 011 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 012 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 013 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 014 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 015 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 016 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 017 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 018 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 019 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 020 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0












F14F12F3 F9F7

F20

F5

F8

F4F10

F11

F2

F15

F1

F13

F19

F18F17

F16F6

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16

Driv

er p

ower

Dependence power

LinkageIndependent










and 11988232




211198822211988232 and119882

33 For example the





1) = 03128


3) =






5 Discussion




Goal


W22

W21

W32

W33

D1 D2 D3 D4







6 Conclusions




Table7Superm

atrix

before

convergence

Goal

Dim

ensio

nsFactors

G1198631

1198632

1198633

1198634

F1F2

F3F4

F5F6

F7F8

F9F10

F11

F12

F13

F14

F15

F16

F17

F18

F19

F20

Goal

G

Dim

ensio

ns

1198631

0318

00323

0261

0403

1198632

0248

0624

00345

0239

1198633

0252

0334

0255

00358

1198634

0181

0041

0422

0394

0F1

0216

00

00

00

00

00

00

00095

00

00

00

F20289

00

00

0284

00

00

00

0051

00065

00

00

00

F30136

00

0064

50367

00

00

00

0118

00145

00

00

00

F40246

00

00

00

00

00

00

00242

00

00

00

F50112

00

00

00

00

00

00148

00222

00

00

00

F60237

00

00

00

00

00

00

00

00

00

00

F70267

021

00

00189

00

00

00

0159

00

00

00

00

F80126

00

00

00

00

00

00

00

00

00

00

F90165

029

00

0355

0159

00

00

00

0207

00159

00

00

00

Factors

F10

0204

03590

00

00

00

00

00

00

00

00

00

0F11

0193

00

00

00

00

00

00

00

00

0453

00

F12

0205

00

00

00

00

00

00

00073

00

00

00

F13

0197

00

00

00

00

00

00

00

032

00

00

0F14

0299

0141

00

00

00

00

00

0124

00

00

00

00

F15

0107

00

00

00

00

00

00192

00

00

00547

00

F16

0287

00

00

00

00

00

00

00

00

00

00

F17

0242

00

00

00

00

00

00

00

0285

00

00

0F18

0262

00

00

00

00

00

00

00

0396

00

00

0F19

0020

00

00

00

00

00

00

00

00

00

00

F20

0189

00

00

00

00

00

00

00

00

00

00




















Acknowledgments


References





















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











3 Method




119878 =

1198901

1198902


1198901

1198902

119890119898

[[[[

[

0

12058721

1205871198981

12058712

0

1199111198982

sdot sdot sdot

sdot sdot sdot

dsdot sdot sdot

1205871119899

1205872119899

0

]]]]

]

(1)











119872 = 119878 + 119868

119872119877= 119872119896= 119872119896+1

119896 gt 1

(2)







119894 Consider

119877 (119905119894) = 119890

119894| 1205871198981198991015840 = 1 (3)

119860 (119905119894) = 119890

119894| 1205871198981015840119899= 1 (4)


119894)


119894) cap 119860(119905

119894)



4 The


119878 =

1198901

1198902

1198903

1198904

1198901

1198902

1198903

1198904

[[[

[

0

1

1

0

1

0

1

0

0

0

0

0

0

1

0

0

]]]

]

119872 = 119878 + 119868 =

1198901

1198902

1198903

1198904

1198901

1198902

1198903

1198904

[[[

[

1

1

1

0

1

1

1

0

0

0

1

0

0

1

0

1

]]]

]

(5)



119890119899

119877 (119905119894) 119860 (119905

119894) 119877 (119905

119894) cap 119860 (119905

119894) Level

1 1 2 4 1 2 3 1 2 22 1 2 4 1 2 3 1 2 23 1 2 3 4 3 3 34 4 1 2 3 4 4 1


119872 = (119878 + 119868)2=

1198901

1198902

1198903

1198904

1198901

1198902

1198903

1198904

[[[

[

1

1

1

0

1

1

1

0

0

0

1

0

1lowast

1

1lowast

1

]]]

]

(6)


119894) cap 119860(119905






119901 119901 = 1 119870 has 119899


by 1198901199011

1198901199012

119890119901119899119901


119882 =

1198621

1198622


11989011 11989012 119890

11198991

11989021 11989022 119890

21198992

sdot sdot sdot 1198901198701 1198901198702 119890

119870119899119870

1198621

11989011

11989012

11989011198991

1198622

11989021

11989022

11989021198992

119862119870

1198901198701

1198901198702

119890119870119899119870

[[[[[[[[[[[[[[[[[[[[

[

11990811

11990821

1199081198701

11990812

11990822

1199081198702

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1199081119870

1199082119870

119908119870119870

]]]]]]]]]]]]]]]]]]]]

]

(7)


119882 = [

[

119868 0 0

11990821

0 0

0 11990832

119868

]

]

(8)







119882 = [

[

119868 0 0

11990821

11990822

0

0 11990832

119868

]

]

(9)


119896rarrinfin(1119873)119882

119896

119895


which 119882infin

= 119908infin







119882infin


(

(

0 0 0

119882119896

2211988221

119882119896

220

11988232(

119896minus2

sum

ℎ=0

119882ℎ

22) 11988232(

119896minus1

sum

ℎ=0

119882ℎ

22) 119868

)

)

(10)




119882infin

= (

0 0 0

0 0 0

11988232(119868 minus 119882

22)minus1

11988221

11988232(119868 minus 119882

22)minus1

119868

)

(11)



4 Case Study



2)






Dimensions Factors


1)







4)








Factors 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 201 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 02 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 03 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 04 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 05 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 07 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 08 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 09 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 010 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 011 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 012 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 013 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 014 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 015 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 016 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 017 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 018 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 019 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 020 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0












F14F12F3 F9F7

F20

F5

F8

F4F10

F11

F2

F15

F1

F13

F19

F18F17

F16F6

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16

Driv

er p

ower

Dependence power

LinkageIndependent










and 11988232




211198822211988232 and119882

33 For example the





1) = 03128


3) =






5 Discussion




Goal


W22

W21

W32

W33

D1 D2 D3 D4







6 Conclusions




Table7Superm

atrix

before

convergence

Goal

Dim

ensio

nsFactors

G1198631

1198632

1198633

1198634

F1F2

F3F4

F5F6

F7F8

F9F10

F11

F12

F13

F14

F15

F16

F17

F18

F19

F20

Goal

G

Dim

ensio

ns

1198631

0318

00323

0261

0403

1198632

0248

0624

00345

0239

1198633

0252

0334

0255

00358

1198634

0181

0041

0422

0394

0F1

0216

00

00

00

00

00

00

00095

00

00

00

F20289

00

00

0284

00

00

00

0051

00065

00

00

00

F30136

00

0064

50367

00

00

00

0118

00145

00

00

00

F40246

00

00

00

00

00

00

00242

00

00

00

F50112

00

00

00

00

00

00148

00222

00

00

00

F60237

00

00

00

00

00

00

00

00

00

00

F70267

021

00

00189

00

00

00

0159

00

00

00

00

F80126

00

00

00

00

00

00

00

00

00

00

F90165

029

00

0355

0159

00

00

00

0207

00159

00

00

00

Factors

F10

0204

03590

00

00

00

00

00

00

00

00

00

0F11

0193

00

00

00

00

00

00

00

00

0453

00

F12

0205

00

00

00

00

00

00

00073

00

00

00

F13

0197

00

00

00

00

00

00

00

032

00

00

0F14

0299

0141

00

00

00

00

00

0124

00

00

00

00

F15

0107

00

00

00

00

00

00192

00

00

00547

00

F16

0287

00

00

00

00

00

00

00

00

00

00

F17

0242

00

00

00

00

00

00

00

0285

00

00

0F18

0262

00

00

00

00

00

00

00

0396

00

00

0F19

0020

00

00

00

00

00

00

00

00

00

00

F20

0189

00

00

00

00

00

00

00

00

00

00




















Acknowledgments


References





















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119890119899

119877 (119905119894) 119860 (119905

119894) 119877 (119905

119894) cap 119860 (119905

119894) Level

1 1 2 4 1 2 3 1 2 22 1 2 4 1 2 3 1 2 23 1 2 3 4 3 3 34 4 1 2 3 4 4 1


119872 = (119878 + 119868)2=

1198901

1198902

1198903

1198904

1198901

1198902

1198903

1198904

[[[

[

1

1

1

0

1

1

1

0

0

0

1

0

1lowast

1

1lowast

1

]]]

]

(6)


119894) cap 119860(119905






119901 119901 = 1 119870 has 119899


by 1198901199011

1198901199012

119890119901119899119901


119882 =

1198621

1198622


11989011 11989012 119890

11198991

11989021 11989022 119890

21198992

sdot sdot sdot 1198901198701 1198901198702 119890

119870119899119870

1198621

11989011

11989012

11989011198991

1198622

11989021

11989022

11989021198992

119862119870

1198901198701

1198901198702

119890119870119899119870

[[[[[[[[[[[[[[[[[[[[

[

11990811

11990821

1199081198701

11990812

11990822

1199081198702

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1199081119870

1199082119870

119908119870119870

]]]]]]]]]]]]]]]]]]]]

]

(7)


119882 = [

[

119868 0 0

11990821

0 0

0 11990832

119868

]

]

(8)







119882 = [

[

119868 0 0

11990821

11990822

0

0 11990832

119868

]

]

(9)


119896rarrinfin(1119873)119882

119896

119895


which 119882infin

= 119908infin







119882infin


(

(

0 0 0

119882119896

2211988221

119882119896

220

11988232(

119896minus2

sum

ℎ=0

119882ℎ

22) 11988232(

119896minus1

sum

ℎ=0

119882ℎ

22) 119868

)

)

(10)




119882infin

= (

0 0 0

0 0 0

11988232(119868 minus 119882

22)minus1

11988221

11988232(119868 minus 119882

22)minus1

119868

)

(11)



4 Case Study



2)






Dimensions Factors


1)







4)








Factors 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 201 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 02 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 03 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 04 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 05 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 07 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 08 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 09 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 010 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 011 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 012 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 013 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 014 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 015 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 016 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 017 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 018 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 019 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 020 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0












F14F12F3 F9F7

F20

F5

F8

F4F10

F11

F2

F15

F1

F13

F19

F18F17

F16F6

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16

Driv

er p

ower

Dependence power

LinkageIndependent










and 11988232




211198822211988232 and119882

33 For example the





1) = 03128


3) =






5 Discussion




Goal


W22

W21

W32

W33

D1 D2 D3 D4







6 Conclusions




Table7Superm

atrix

before

convergence

Goal

Dim

ensio

nsFactors

G1198631

1198632

1198633

1198634

F1F2

F3F4

F5F6

F7F8

F9F10

F11

F12

F13

F14

F15

F16

F17

F18

F19

F20

Goal

G

Dim

ensio

ns

1198631

0318

00323

0261

0403

1198632

0248

0624

00345

0239

1198633

0252

0334

0255

00358

1198634

0181

0041

0422

0394

0F1

0216

00

00

00

00

00

00

00095

00

00

00

F20289

00

00

0284

00

00

00

0051

00065

00

00

00

F30136

00

0064

50367

00

00

00

0118

00145

00

00

00

F40246

00

00

00

00

00

00

00242

00

00

00

F50112

00

00

00

00

00

00148

00222

00

00

00

F60237

00

00

00

00

00

00

00

00

00

00

F70267

021

00

00189

00

00

00

0159

00

00

00

00

F80126

00

00

00

00

00

00

00

00

00

00

F90165

029

00

0355

0159

00

00

00

0207

00159

00

00

00

Factors

F10

0204

03590

00

00

00

00

00

00

00

00

00

0F11

0193

00

00

00

00

00

00

00

00

0453

00

F12

0205

00

00

00

00

00

00

00073

00

00

00

F13

0197

00

00

00

00

00

00

00

032

00

00

0F14

0299

0141

00

00

00

00

00

0124

00

00

00

00

F15

0107

00

00

00

00

00

00192

00

00

00547

00

F16

0287

00

00

00

00

00

00

00

00

00

00

F17

0242

00

00

00

00

00

00

00

0285

00

00

0F18

0262

00

00

00

00

00

00

00

0396

00

00

0F19

0020

00

00

00

00

00

00

00

00

00

00

F20

0189

00

00

00

00

00

00

00

00

00

00




















Acknowledgments


References





















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra














119882infin


(

(

0 0 0

119882119896

2211988221

119882119896

220

11988232(

119896minus2

sum

ℎ=0

119882ℎ

22) 11988232(

119896minus1

sum

ℎ=0

119882ℎ

22) 119868

)

)

(10)




119882infin

= (

0 0 0

0 0 0

11988232(119868 minus 119882

22)minus1

11988221

11988232(119868 minus 119882

22)minus1

119868

)

(11)



4 Case Study



2)






Dimensions Factors


1)







4)








Factors 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 201 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 02 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 03 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 04 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 05 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 07 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 08 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 09 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 010 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 011 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 012 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 013 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 014 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 015 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 016 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 017 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 018 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 019 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 020 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0












F14F12F3 F9F7

F20

F5

F8

F4F10

F11

F2

F15

F1

F13

F19

F18F17

F16F6

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16

Driv

er p

ower

Dependence power

LinkageIndependent










and 11988232




211198822211988232 and119882

33 For example the





1) = 03128


3) =






5 Discussion




Goal


W22

W21

W32

W33

D1 D2 D3 D4







6 Conclusions




Table7Superm

atrix

before

convergence

Goal

Dim

ensio

nsFactors

G1198631

1198632

1198633

1198634

F1F2

F3F4

F5F6

F7F8

F9F10

F11

F12

F13

F14

F15

F16

F17

F18

F19

F20

Goal

G

Dim

ensio

ns

1198631

0318

00323

0261

0403

1198632

0248

0624

00345

0239

1198633

0252

0334

0255

00358

1198634

0181

0041

0422

0394

0F1

0216

00

00

00

00

00

00

00095

00

00

00

F20289

00

00

0284

00

00

00

0051

00065

00

00

00

F30136

00

0064

50367

00

00

00

0118

00145

00

00

00

F40246

00

00

00

00

00

00

00242

00

00

00

F50112

00

00

00

00

00

00148

00222

00

00

00

F60237

00

00

00

00

00

00

00

00

00

00

F70267

021

00

00189

00

00

00

0159

00

00

00

00

F80126

00

00

00

00

00

00

00

00

00

00

F90165

029

00

0355

0159

00

00

00

0207

00159

00

00

00

Factors

F10

0204

03590

00

00

00

00

00

00

00

00

00

0F11

0193

00

00

00

00

00

00

00

00

0453

00

F12

0205

00

00

00

00

00

00

00073

00

00

00

F13

0197

00

00

00

00

00

00

00

032

00

00

0F14

0299

0141

00

00

00

00

00

0124

00

00

00

00

F15

0107

00

00

00

00

00

00192

00

00

00547

00

F16

0287

00

00

00

00

00

00

00

00

00

00

F17

0242

00

00

00

00

00

00

00

0285

00

00

0F18

0262

00

00

00

00

00

00

00

0396

00

00

0F19

0020

00

00

00

00

00

00

00

00

00

00

F20

0189

00

00

00

00

00

00

00

00

00

00




















Acknowledgments


References





















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Factors 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 201 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 02 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 03 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 04 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 05 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 07 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 08 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 09 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 010 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 011 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 012 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 013 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 014 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 015 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 016 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 017 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 018 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 019 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 020 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0












F14F12F3 F9F7

F20

F5

F8

F4F10

F11

F2

F15

F1

F13

F19

F18F17

F16F6

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16

Driv

er p

ower

Dependence power

LinkageIndependent










and 11988232




211198822211988232 and119882

33 For example the





1) = 03128


3) =






5 Discussion




Goal


W22

W21

W32

W33

D1 D2 D3 D4







6 Conclusions




Table7Superm

atrix

before

convergence

Goal

Dim

ensio

nsFactors

G1198631

1198632

1198633

1198634

F1F2

F3F4

F5F6

F7F8

F9F10

F11

F12

F13

F14

F15

F16

F17

F18

F19

F20

Goal

G

Dim

ensio

ns

1198631

0318

00323

0261

0403

1198632

0248

0624

00345

0239

1198633

0252

0334

0255

00358

1198634

0181

0041

0422

0394

0F1

0216

00

00

00

00

00

00

00095

00

00

00

F20289

00

00

0284

00

00

00

0051

00065

00

00

00

F30136

00

0064

50367

00

00

00

0118

00145

00

00

00

F40246

00

00

00

00

00

00

00242

00

00

00

F50112

00

00

00

00

00

00148

00222

00

00

00

F60237

00

00

00

00

00

00

00

00

00

00

F70267

021

00

00189

00

00

00

0159

00

00

00

00

F80126

00

00

00

00

00

00

00

00

00

00

F90165

029

00

0355

0159

00

00

00

0207

00159

00

00

00

Factors

F10

0204

03590

00

00

00

00

00

00

00

00

00

0F11

0193

00

00

00

00

00

00

00

00

0453

00

F12

0205

00

00

00

00

00

00

00073

00

00

00

F13

0197

00

00

00

00

00

00

00

032

00

00

0F14

0299

0141

00

00

00

00

00

0124

00

00

00

00

F15

0107

00

00

00

00

00

00192

00

00

00547

00

F16

0287

00

00

00

00

00

00

00

00

00

00

F17

0242

00

00

00

00

00

00

00

0285

00

00

0F18

0262

00

00

00

00

00

00

00

0396

00

00

0F19

0020

00

00

00

00

00

00

00

00

00

00

F20

0189

00

00

00

00

00

00

00

00

00

00




















Acknowledgments


References





















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


















F14F12F3 F9F7

F20

F5

F8

F4F10

F11

F2

F15

F1

F13

F19

F18F17

F16F6

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16

Driv

er p

ower

Dependence power

LinkageIndependent










and 11988232




211198822211988232 and119882

33 For example the





1) = 03128


3) =






5 Discussion




Goal


W22

W21

W32

W33

D1 D2 D3 D4







6 Conclusions




Table7Superm

atrix

before

convergence

Goal

Dim

ensio

nsFactors

G1198631

1198632

1198633

1198634

F1F2

F3F4

F5F6

F7F8

F9F10

F11

F12

F13

F14

F15

F16

F17

F18

F19

F20

Goal

G

Dim

ensio

ns

1198631

0318

00323

0261

0403

1198632

0248

0624

00345

0239

1198633

0252

0334

0255

00358

1198634

0181

0041

0422

0394

0F1

0216

00

00

00

00

00

00

00095

00

00

00

F20289

00

00

0284

00

00

00

0051

00065

00

00

00

F30136

00

0064

50367

00

00

00

0118

00145

00

00

00

F40246

00

00

00

00

00

00

00242

00

00

00

F50112

00

00

00

00

00

00148

00222

00

00

00

F60237

00

00

00

00

00

00

00

00

00

00

F70267

021

00

00189

00

00

00

0159

00

00

00

00

F80126

00

00

00

00

00

00

00

00

00

00

F90165

029

00

0355

0159

00

00

00

0207

00159

00

00

00

Factors

F10

0204

03590

00

00

00

00

00

00

00

00

00

0F11

0193

00

00

00

00

00

00

00

00

0453

00

F12

0205

00

00

00

00

00

00

00073

00

00

00

F13

0197

00

00

00

00

00

00

00

032

00

00

0F14

0299

0141

00

00

00

00

00

0124

00

00

00

00

F15

0107

00

00

00

00

00

00192

00

00

00547

00

F16

0287

00

00

00

00

00

00

00

00

00

00

F17

0242

00

00

00

00

00

00

00

0285

00

00

0F18

0262

00

00

00

00

00

00

00

0396

00

00

0F19

0020

00

00

00

00

00

00

00

00

00

00

F20

0189

00

00

00

00

00

00

00

00

00

00




















Acknowledgments


References





















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Goal


W22

W21

W32

W33

D1 D2 D3 D4







6 Conclusions




Table7Superm

atrix

before

convergence

Goal

Dim

ensio

nsFactors

G1198631

1198632

1198633

1198634

F1F2

F3F4

F5F6

F7F8

F9F10

F11

F12

F13

F14

F15

F16

F17

F18

F19

F20

Goal

G

Dim

ensio

ns

1198631

0318

00323

0261

0403

1198632

0248

0624

00345

0239

1198633

0252

0334

0255

00358

1198634

0181

0041

0422

0394

0F1

0216

00

00

00

00

00

00

00095

00

00

00

F20289

00

00

0284

00

00

00

0051

00065

00

00

00

F30136

00

0064

50367

00

00

00

0118

00145

00

00

00

F40246

00

00

00

00

00

00

00242

00

00

00

F50112

00

00

00

00

00

00148

00222

00

00

00

F60237

00

00

00

00

00

00

00

00

00

00

F70267

021

00

00189

00

00

00

0159

00

00

00

00

F80126

00

00

00

00

00

00

00

00

00

00

F90165

029

00

0355

0159

00

00

00

0207

00159

00

00

00

Factors

F10

0204

03590

00

00

00

00

00

00

00

00

00

0F11

0193

00

00

00

00

00

00

00

00

0453

00

F12

0205

00

00

00

00

00

00

00073

00

00

00

F13

0197

00

00

00

00

00

00

00

032

00

00

0F14

0299

0141

00

00

00

00

00

0124

00

00

00

00

F15

0107

00

00

00

00

00

00192

00

00

00547

00

F16

0287

00

00

00

00

00

00

00

00

00

00

F17

0242

00

00

00

00

00

00

00

0285

00

00

0F18

0262

00

00

00

00

00

00

00

0396

00

00

0F19

0020

00

00

00

00

00

00

00

00

00

00

F20

0189

00

00

00

00

00

00

00

00

00

00




















Acknowledgments


References





















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table7Superm

atrix

before

convergence

Goal

Dim

ensio

nsFactors

G1198631

1198632

1198633

1198634

F1F2

F3F4

F5F6

F7F8

F9F10

F11

F12

F13

F14

F15

F16

F17

F18

F19

F20

Goal

G

Dim

ensio

ns

1198631

0318

00323

0261

0403

1198632

0248

0624

00345

0239

1198633

0252

0334

0255

00358

1198634

0181

0041

0422

0394

0F1

0216

00

00

00

00

00

00

00095

00

00

00

F20289

00

00

0284

00

00

00

0051

00065

00

00

00

F30136

00

0064

50367

00

00

00

0118

00145

00

00

00

F40246

00

00

00

00

00

00

00242

00

00

00

F50112

00

00

00

00

00

00148

00222

00

00

00

F60237

00

00

00

00

00

00

00

00

00

00

F70267

021

00

00189

00

00

00

0159

00

00

00

00

F80126

00

00

00

00

00

00

00

00

00

00

F90165

029

00

0355

0159

00

00

00

0207

00159

00

00

00

Factors

F10

0204

03590

00

00

00

00

00

00

00

00

00

0F11

0193

00

00

00

00

00

00

00

00

0453

00

F12

0205

00

00

00

00

00

00

00073

00

00

00

F13

0197

00

00

00

00

00

00

00

032

00

00

0F14

0299

0141

00

00

00

00

00

0124

00

00

00

00

F15

0107

00

00

00

00

00

00192

00

00

00547

00

F16

0287

00

00

00

00

00

00

00

00

00

00

F17

0242

00

00

00

00

00

00

00

0285

00

00

0F18

0262

00

00

00

00

00

00

00

0396

00

00

0F19

0020

00

00

00

00

00

00

00

00

00

00

F20

0189

00

00

00

00

00

00

00

00

00

00




















Acknowledgments


References





















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra




























Acknowledgments


References





















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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