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Scientific Research and Essays Vol. 6(25), pp. 5374-5386, 30 October, 2011 Available online at http://www.academicjournals.org/SREISSN 1992-2248 ©2011 Academic Journals

Full Length Research Paper

A new fuzzy mathematical model for multi criteriadecision making: An application of fuzzy mathematical

model in a SWOT analysis

Dragan Pamučar 1*, Goran Ćirović2, Dragoljub Sekulović3 and Aleksandar Ilić4

1Management Department,

University of Defence, Military Academy,

Generala Pavla Jurisica Sturma 33, 11 000,

Belgrade, Serbia.2Faculty of Technical Science, University of Novi Sad, Novi Sad, Serbia.

3

Architectural and Civil Engineering Faculty, Banja Luka, Bosnia and Herzegovina.4Department of Material Resources,

Ministry of Defence, Belgrade, Serbia.

Accepted 20 September, 2011

Analysis of strengths, weaknesses, opportunities and threats (SWOT) is a method to formulate thestrategy. Although the SWOT analysis successfully provides the key factors of the problem, it has somedrawbacks in selecting appropriate strategy for the evaluation and final decision steps. During recentyears, some multiple criteria decision making (MCDM) remove some of these deficiencies, but thenature of these decision usually is very complex and using crisp datais not suitable. In this paper,linguistic variable represented with fuzzy numbers are used to assess the ratings and weights. Thispaper presents a new fuzzy mathematical model for evaluating the proposed alternatives. Fuzzylinguistic descriptors were used for describing the criteria. In this way, fuzzy logic enables theexploitation of tolerance that exists in imprecision, uncertainty and partial truth of the acquired

research results. The paper presents a model for designing the organisational structure of transportsupport authorities in the Serbian Armed Forces. Various organisational structure options are proposedin application of the given model, taking into account the fact that transport authorities should bedesigned and dimensioned so as to achieve the rudimentary goals and tasks for fulfilment of whichthey were established. Each task set before the transport authorities requires reliable and top-qualityperformance in all environmental conditions. Since most of the acquired data is characterized by a highdegree of imprecision, subjectivity and uncertainty, fuzzy logic was used for displaying these.

Key words: Strengths, weaknesses, opportunities and threats analysis, organizational structure design, fuzzylogic, multi-criteria decision making.

INTRODUCTION

Strategic management is the process by which managersformulate and implement strategies that enableorganisations to achieve strategic objectives. Strategicmanagement in the broadest sense can be defined as theconscious direction of the business system consistentwith its relevant environment. In accordance with the

*Corresponding author. E-mail: [email protected]. Tel:+38164 23 77 908, +38111 251 92 89. Fax: +38111 300 51 90.

current reforms of the defence system of the Republic ofSerbia, the Serbian Armed Forces are gradually leavingthe outdated principles of organisation and operation ologistical support and embracing a modern logisticconcept. In this sense, properly structured system oforganisational management solutions to a large extencontribute to the functional efficiency of these systemsproviding corresponding cost savings. In the process oreorganisation of the Serbian Armed Forces, there arestill some organisational forms proven inefficient in thepast and in particular unsuited for the future. Inefficien



and uneconomic operation demands adequate solutions.The process of transport authorities administrativesupport reorganisation requires a design team, time andfinancial resources. This paper presents a model ofdesigning organisational scheme of administrativestructure of the Serbian Armed Forces. In complex

organisational systems operating in a changingenvironment such as the armed forces, a large number ofissues whose solutions are accompanied with differenttypes of imprecision and uncertainty exist at all levels ofmanagement. They can be described using linguisticexpressions and modelled by uncertain numbers. In theclassical approach, uncertainty modelling is based on theapplication of probability theory, where uncertainty ismodelled in random sizes with different distribution. Thismanner of uncertainty treatment has certain limitations.One is that the probability calculation of any random sizerequires a large quantity of the data recorded, and alsothe fact that the combination of different uncertaintiesleads to a complex probability distribution, which requirescomplex mathematical expressions and increases thecomplexity and volume of calculations.Development of new mathematical areas facilitateddescribing imprecision and uncertainty in a more realisticway. In other words, soft computing methods arealternatives to the classical approach in uncertaintytreatment. One of the methods of soft computing is thefuzzy theory. Designing organisations, in particular thestage of organisational model development is a highlycomplex process in which optimal solutions should beoffered. SWOT analysis is a useful "tool" for planningdesign strategies in which organisational internalstrengths and weaknesses are weighed against the

external opportunities and threats. The organisationshould mobilise its forces, overcome weaknesses, exploitopportunities and resist threats. Associating opportunitiesand risks on one hand and strengths and weaknesses onthe other, the organisation aims at providing a conceptualframework for the selection of strategic options of theorganisational model. However, the result of SWOTanalysis is often merely a listing or an incompletequalitative examination of the internal and externalfactors. For this reason, SWOT analysis cannotcomprehensively appraise the strategic-making process.

Applying fuzzy multi-criteria decision making (FMDM) inthe SWOT analysis eliminates the weakness in the

measurement and evaluation steps of the SWOTanalysis.

MULTICRITERIA MATHEMATICAL METHODS

Multiple criteria decision making refers to decisionmaking in a situation with a number of possiblyconflicting criteria. This is the greatest advantage ofmultiple criteria decision making, since in practicethere are a few problems influenced by one factor only,

Pamucar et al. 5375

or in other words, whose optimization includes just onecriterion. The main goal of multiple criteria methods isdetermination of the priorities among specific variantsor criteria in situations where a number of decisionmakers are taking part, and where there are a numberof decision making criteria and multiple time periods

There are many ways to classify the methods of multiplecriteria decision making. However, the classification ofthese methods in accordance with those ways is oftenavoided because the models in accordance to whichthese methods operate are quite similar. Their enlisting isfavoured instead. The most frequently used methods are:

i) Points method,ii) ELECTRE method,iii) PROMETHEE method,iv) TOPSIS method,v) AHP method (analytic of hierarchical processes),vi) Fuzzy multicriteria decision making,vii) ANFIS models,viii) Models based on neuron networks,ix) Models based on fuzzification of the already existingmultiple criteria decision making methods.

The choice of evaluation methods depends on:

i) Character, that is importance of the decision to bemade on the basis of evaluation,ii) The place where the decision is to be made,iii) Kind of the decision because of which evaluation isbeing made,iv) The ways of financing implementation of a newsolution (finance construction).

In case of a responsible decision making, speciamethods for multiple criteria analysis and indirecoptimization are commonly used. The methods of sofoptimization are used in the first place to describemultiple objectives, with some of them being maximizedand others minimized. Then, conflicts of prioritiesbetween the different participants in decision makingprocess are modelled, and at the end, a solution that isthe closest to the ideal point, the best compromise, etc. issearched for. Most often, decision making meansevaluation of sets of possible solutions or alternativesWhen evaluation is made in accordance with one

criterion, the solution (alternative) which brings the targetfunction to an extreme is determined and the procedureis denoted as single criterion optimization or simplyoptimization. The situation is getting more complex withtwo or more criteria, when instead of the optimal solutionthe best possible solution needs to be provided. Anygrouping of the criteria into one criterion (totascalarisation) and reducing the task to a single criteriongenerates deficiencies limiting the range of the analysisand the accuracy of the results. Instead of totascalarisation, a multiple criteria problem is usually deal



5376 Sci. Res. Essays

with in its original form, while the level of target functionscalarisation is controlled by the decision maker or theanalyst. In other words, the decision maker oftenevaluates criteria against each other, or attaches theranks of importance directly, thus shaping the targetfunction in accordance with his own preferences.

Regardless whether it is done directly or indirectly, in thegiven phase of the decision making process, a matrix ofalternatives and criteria is created. This matrix isanalysed and processed so that weighing grades for thealternatives, based on which they can be ranked may beestablished.

The weighing grades and ranks may be usedindividually or integrally, depending on the kind of aproblem. If only the best alternative is searched for, onlyranking will mostly suffice. With respect to allocationproblems, grades can signify the proportions of allocationresources in accordance with the ranks of thealternatives. The third possibility is that identification ofseveral best alternatives and the degree to which theyparticipate in the total resource allocation are searchedfor. Multiple criteria and hierarchical structures are part ofa complex environment facing analysts when they dealwith problems of decision making and creation of qualitymethods for their resolution in practice. The presence ofdifferent criteria, some of which have to be maximisedand some minimized, means that decisions are made inthe conflicting conditions and that instruments moreflexible than a rigid mathematical technique related togenuine optimization have to be applied. Special analysisand solution techniques have been developed for suchtasks. Among the most important are PROMETHEE(Brans et al., 1986), ELECTRE (Roy, 1968), AHP (Saaty,

1980), TOPSIS (Hwang and Yoon, 1981) and CP(Zeleny, 1982). These techniques fall into the category ofsoft optimization, since they use heuristic parameters,distance measurements, value scales, etc. in addition tomathematical structures and instruments. Kujacić andBojović (2003) proposed the model for selecting theorganisational structure using the fuzzy multi-criteriaanalysis. The developed fuzzy multi-criteria methodologytakes into consideration the uncertainty and imprecisionof the input data. Each method earlier mentioned hasseveral versions (for example, Promethee 1 and 2). Theyall have advantages and disadvantages and theirapplication in different areas indicates that those methods

are getting increasingly indispensible in backingresponsible decision making.

Recently, standard and fuzzy versions of methods areused in parallel so that the complex of humansubjectivity, expert knowledge and inclination to useverbal instead of numerical grades may be included(Triantaphyllou and Lin, 1996; Bender and Simonovic,2000; Deng, 1999; Srđevic et al., 2002; Pamučar, 2009).The methods used for modelling subjectivism,approximate reasoning and expert knowledge of decisionmakers, as well as various forms of heuristics are part of

relatively recent decision making climate in the ArmedForces of Serbia. This climate has brought newterminology and in a certain way a new application ofmathematics and optimization theory in the realisticconditions of planning and decision making. In the ArmedForces of Serbia today, standard and fuzzy versions o

multiple criteria methods are used in parallel, but newmodels of multiple criteria decision making based onfuzzy logic modelling and neuro-fuzzy modelling arebeing developed (Pamučar and Božanić, 2010; Pamučar2009, 2010; Pamučar et al., 2011). By modelling of fuzzylogic systems and training of the neuro-fuzzy model, verypowerful tools for decision making, based on experientiaknowledge of the officers of the Armed Forces of Serbiaare created. Officers experiential knowledge istransformed to automatic management (decision making)strategy through modelling of such systems. Fuzzy setsenable quantification of linguistic; that is qualitative andinaccurate information. Therefore, fuzzy reasoning isincreasingly used in the Armed Forces of Serbia as atechnique by which heuristic rules are translated intoautomatic management; that is decision making, strategy

Application of the fuzzy theory and fuzzy sets in multicriteria decision making has come into use since decisionmakers often act in the conditions of uncertainty or socalled partial truths.

Fuzzification of standard multiple criteria methods wasdone in such a way that triangular fuzzy numbers wereused for determination of fuzzy weighing values focriteria and alternatives, due to their simplicity incomparison to trapezoid ones, while altogether, fuzzyarithmetic was, of course, used (Pamučar, 2010). A newfuzzy mathematical method presented in this paper has

been developed for research in the Armed Forces ofSerbia. The developed method is based on evaluation oalternatives by application of fuzzy linguistic descriptorsIt makes the procedure of alternatives ranking mucheasier in situations where a great number ocharacteristics and parameters for decision making arepresent. If there are more levels of criterion importance inthe problem of alternative ranking, the describedprocedure is conducted at each observed level. At eachlevel, the coefficients of criterion- sub criterion importancehaving an impact on the course of ranking is defined, withthe level of ranking being not necessarily the same for althe criteria. The final ranking of the alternatives is made

at ranking zero level. Characteristics of some multiplecriteria methods has been presented in the first part othe paper. In the continuation, a new model for theselection of optimal variants of organisation based onfuzzy logic has been developed starting from the relevanttheory approach. Fuzzy mathematical model (FMM) isapplied in the SWOT analysis (FM'WOT model) tooptimize the existing organisational structure of thegoverning bodies of transport support. The choice oforganisational models is made using Fuzzy multi-criterionand standard techniques of multi-criterion decision



Figure 1. Triangular fuzzy number.

Figure 2. Defuzzification.

making.The aforementioned model is shown in the followingsection of the paper.

FM'WOT MODEL

In the process of designing the organisational structure,

certain decisions have to be made. Subjective evaluationof certain parameters differ from one decision-maker toanother, it is worth pointing out. Quite a convenientapproach in quantifying these parameters is fuzzy settheory.

Fuzzy sets

Fuzzy sets theory defines fuzzy set A as a set of orderedpairs (Zadeh, 1965):

Pamucar et al. 5377

, ,0 1 , A A A x x x X x

Where A x is a membership function which shows to

what extent x X meets the criterions for membership

in a set A . For the membership function

0 1 A x , for every x A ,that is : 0,1 A X .

According to the fuzzy theory, the choice of membershipfunctions that is, the form of the function and confidenceintervals width are usually made based on subjectiveestimates or experience. The most commonly used aretrapezoidal and triangular fuzzy numbers. Triangulafuzzy numbers with membership functions shown inFigure 1 are used in this paper. Triangular fuzzy numbers

are usually given in the form1 2 3

( , , ) A a a a , where 2a is

the value where the membership function of the fuzzy

number is 1.0, 1a is the left distribution of the confidenceinterval and 3a the right distribution of the confidence

interval of the fuzzy number A . Fuzzy number Amembership function is defined as:

1

11 2

2 1

32 3

3 2

3

0,

,

,

0,

A

x a x a

a x aa a

xa x

a x aa a

x a

For defuzzification and mapping of the fuzzy number

1 2 3( , , ) A a a a value into a real numbers, numerous

methods are used (Figure 2). Two methods have beenused in this paper:

i) The centre of gravity:

1

3 1 2 1 1A= 3defuzzy a a a a a

ii) The total integral value:

1

3 2 1A= 1 2defuzzy a a a

(with , 0,1 being an optimism index).

Basic model

It is characteristic for all multi-criteria problems that thereare multiple criteria in decision-making and variousalternatives to select the most appropriate actionDifferent organisations evaluate variant solutions andoptimal variants using the FMM model described in thecontinuation. SWOT analysis is used for assessing wha




to eliminate, partially keep or keep to define designstrategies for designing organisational structure. Usinganalysis of strengths, weaknesses, opportunities andthreats for the given organisation, optimisation model offunctioning is proposed. Fuzzy mathematical modelincludes the following steps:

Step 1

Identify SWOT sub-factors and determinate thealternative strategies according to the SWOT sub-factors: Determine the importance degrees of the SWOTfactors; if the model used for evaluation of alternatives ofthe already proposed organisational structurealternatives, this step is omitted. The following steps will

represent a general case where K is considered fromthe point of different optimality criteria in terms of whichthe best alternative for a finite set of alternatives is

determined 1 2, , , , 2n A a a a n . Optimum

criterions are formally given as 1, , , , K k K ,

where K is the overall number of the criteria considered.Multiple-attribute problem in the decision-making is

represented by the matrix F dimension K A .

1

11 11

1

1

...n m n

n m n

k kn m knk

K Kn m Kn K

A A A

f f f K

F f f f K

f f f K

Where 1, , 1,ki f i A k K is the linguistic or numerical

value of the optimum criterion k K for alternatives

a a A . If at least one criterion is described by

linguistic expression in the description of the optimumcriterion, step 2 is taken.

Step 2

Defining the set of linguistic descriptors: Criterionvalues are described by a set of linguistic descriptors

1 2, , , , 0, ,iS l l l i H T , where T is the

overall number of linguistic descriptors. Linguistic

variables are represented by triangular fuzzy numbers

1 2 3( , , ) A a a a .

Step 3

Normalisation of the optimisation criterion: For the

value 1, , 1,ki

f i A k K to be comparable, it is

necessary to normalise them. If the optimisation criteria

are given as linguistic values 1, , 1,ki

f i A k K

,

kiki ki f

f f , normalisation is performed as follows:

i) For the benefit criterion k k K normalisation is

performed as follows:

max

k k n

k

ii

f f

f (1)

Wheremax

k f is max value of the fuzzy numbe

( 1, , )ki f k K , for 0

ki ki f

f

ii) For the cost criterion k k K normalisation is

performed as follows:

min

max1 ki k ik n

k

f f f f

(2)

Wheremin

k f is minimum value of the fuzzy numbe

( 1, , )ki f k K , for 0

ki ki f

f .

The normalised value of the criterion ( )k k K for

( )a a A alternative is described by fuzzy number:

,ik

ik ik f n

n

f f (3)

If the optimality criteria are described in numerical values

1, , 1,ki

f i A k K , normalisation is performed as

follows:

11

, 1k ki

K ki

ki ki

k

K

f

f f f

(4)



Step 4

Evaluation criteria: 1, , , , K k K is a set of

optimality criteria, where K is the overall number of theconsidered criteria. Every criterion can be disaggregated

into sub-criteria. If jk is the overall number of sub-criteriain j th

criterion, the overall number of criterions can be

given as:

1

n

j

j

K k

(5)

Every criterion has to be divided into sub-criteria. In that

case jk of the criterion equals 1. This is important for

understanding the aggregation process of judgmentsmade at two consecutive hierarchical levels, where

criteria and sub-criteria are located. Here, criteria andsub-criteria are aggregated by shifting criteria at the sub-criteria level. After that shift, the whole criteria level doesnot exist anymore. Relative importance of the optimality

criterion , 1, ,k k k K W k K is different. The

value representing the importance of the optimality

criteria is determined by forming a matrix

K K kijwW

.

Elements of the matrix are linguistic descriptors andnumerical values used to describe the importance of the

criterion k k K to criterion k k K . Having

establishedW

matrix, normalisation of the weight

coefficients is performed:

1

1

, 1, 0,1

j

j

K j k

j

kij k k K

j k j

w w ww

w

ò (6)

Where j represents the preference of decision maker to

attribute i .

The process of designing the organisational structure ismost often in the hands of more than one expert that isdecision-maker. In this case, optimality criteria evaluationof all the group members should first be obtained to passon to the necessary synthesis and then to step 5. In othercases, step 6 is taken.

Step 5

Evaluating the criteria in case of group evaluation: Ingroup decision-making, there is group synthesis withcomplete and incomplete information. In case of groupsynthesis with complete information, provided that all the

Pamucar et al. 5379

members ( 1,2,..., )e n of the group G are considered

equal in the decision making and that all the evaluation othe optimality criterion for the given hierarchy have beenperformed, there are two ways for prioritising thealternatives relative to the goal. One is to aggregate althe obtained priority criterion vectors for every decision

maker using the following equation:

1

( )n

G

i e i

e

w w e

(7)

Where ( )i

w e is the weight value which is the n th

member of the group G , ( 1,2,..., )e n for the

alternativei A ,

e is the weight value (significance) o

the n th member of the group andG

iw is the ultimate

priority of the alternative i A . Individual weights of the e group members have first been additively normalisedThe drawback of the presented procedure is that it is notapplicable in case of group synthesis with incompleteinformation, as there are no composite vectors for certainmembers of the group.

Another way is to immediately aggregate all theindividual preference assessments on all hierarchicalevels.

11 1 1

11 1 11

j

j

n n nn n nn

j k

i j ij j ij j ij

i j j j j

k

k j

ij K

ww a aw

wa

1

1, 0,1k

j

K

k w w

ò

(8)

Where j

represents the preference of the decision

maker to attribute i .

N case of group synthesis with incomplete information

microaggregation of the ,i j position at the given

matrix is done by geometric mean of the assessments of

those group members who expressed preference i E compared to the element

j E . The requirement in this

case is for at least one decision maker to declare on the

value ofij

a . Modifying the previous expression:

1 11

11 11

j

j

n M G M n n nn

j k G

i j ij j ij j ijkij

il L j j j j

K G

k

ww a l a aw

w

1

1, 0,1k

j

K

k w w

ò

(9)




Where l is a set of group members who have evaluated

the pair of elements ,i j E E and M is the number of

such members.

Step 6

Evaluating alternatives: Having determined the valuesof the weight coefficients for all the assessed criterions, a

matrix

F W ijc F

is formed where the matrix elements

ijc are obtained using the following expression:

1

ijij k j

ki

kii

f

f c w

(10)

Where

ki f

is the value of the criterion function for the

alternative( 1, )i i A

and criterion k k K

, and

ijk w

is the value of the weight coefficient for the criterion

k k K .

Additive synthesis has been assumed here and thefinal alternative performance weights with respect tooverall goal are calculated by the summation of elements

in the rows of the performance matrix

F W ijc F

as:

1

K

i ij j

j

c c w

(11)

Value of the criterion functions iV for every assessed

alternative is obtained from the F matrix using theexpression:

1

, ( ) j

K

i j

V c k K

(12)

To finally rank the alternatives, the prioritisation of

aggregated assessments is required. Since each iV is a

triangular fuzzy number, it is necessary to apply themethod of ranking triangular fuzzy numbers. There areseveral methods that can do this such as the centre ofgravity method, the dominance measure method, the -cut with interval synthesis method and the total integralvalue method. The last one – total integral value method

(Liou and Wang, 1992) is considered to be a good choicefor performing the task efficiently and, therefore, hasbeen proposed within this methodology. For the given

triangular fuzzy number 1 2 3( , , ) A a a a, the tota

integral value is defined as:

1

3 2 1I (A)= 1 2 , 0,1T

a a a

(13)

In Equation 13, represents an optimism index which

expresses the decision maker’s attitude towards risk. A

larger value of indicates a higher degree of optimism

In practical applications, values 0, 0.5 and 1 are usedrespectively to represent the pessimistic, moderate andoptimistic views of the decision maker. For given fuzzy

numbers A and B , it is said that if I (A)<I (B)T T

then A B ; if I (A) I (B)T T then A B ; and i

I (A) I (B)T T

, then A B . The final ranking o

alternatives means to adopt certain level λ of optimism othe decision-maker, then to apply Equation 13 on fuzzynumbers of Equation 12 and finally to rank alternatives

regarding obtained values for I ( ), 1,...,T i F i N

The best alternative from the set is represented as

max , 1,..,i iV V f f i A

. The presented

method significantly simplifies the procedure of rankingthe alternatives in situations where there are a number ofcharacteristics and parameters of decision making. Onthe basis of the proposed algorithm, a system for

decision support in the programming language C wasdeveloped.

DESIGNING THE MANAGEMENT ORGANISATIONALSTRUCTURE OF THE TRAFFIC SUPPORT USINGFM'WOT MODEL

Designing a military management system has a large

influence on the creation, adaptation, existence andquality of the system operation. No organisational systemwithin the military can operate independently of itsmanagement subsystem responsible for issuingcommands for the desired “behaviour” of the systemwhile the actual behaviour can deviate from the desiredTo meet the requirements of a large number of traffic andtransport services users and at the same time efficientlyand primarily servicing the requirements of the militaryan organisational structure that will successfullyimplement all these must exist. As part of the GeneraStaff and the Logistics Department, traffic management is



the highest professional traffic authority of the Serbian Armed Forces. Traffic management is responsible andaccountable for the conditions, development,management, organisation, monitoring, training,normative regulation and traffic control support and othertasks within its competence. Events from the 90's, called

for a review of the organisational structure of thetransport support governing bodies. This situationhighlights the need for further study of the organisationalstructure of traffic management.

An illustrative application of SWOT analysis

This section presents an illustration of the proposedapproach summarized previously. In order to define thegoverning bodies for traffic support design strategy, aSWOT analysis of influence; that is opportunities andthreats from the environment on the management of thetraffic support has been done (Figure 3). SWOT analysis

is used to manage the total organisation, the overallpattern of structural components and arrangement.Having applied the SWOT analysis, four varieties of thetraffic support governing bodies organisational structureare defined:

Alternat ive 1 ( 1 A )

The current organisation of the governing bodies of thetraffic support, defined on the basis of normativeregulation for determining the organisational solutions inthe military formations and experience of thoseparticipating in making decisions. The currentorganisation consists of two organisational units:Department of Traffic Operations and Department ofTransport (Figure 4).

Alternat ive 2 (2 A )

Organisational structure of the governing bodies of thetraffic support after the NATO standard.


Organisational structure established according to theprocesses where organisational units are defined foreach of those processes. Specialists indispensable forimplementing these processes are present in each group.If traffic management is viewed as the governing body ormanagement of the transport support, then it is the holderof the implementation of certain processes.


The structure of the traffic support governing bodies

Pamucar et al. 5381

using the logistic approach and functional principle oforganisation of the prescribed authority, as a specificmanifestation of the internal division of labourdifferentiation and specialisation, organisational units andholders of command and control.

Assessment, synthesis and ranking

First steps in the application of the fuzzy mathematicamodel would be defining the set of linguistic descriptorsLinguistic variables are represented by a set of linguistic

descriptors 1 2{ , ,..., }, {0,1,..., },iS l l l i H T where

T is the overall number of linguistic descriptors. In this

case, the number of linguistic descriptors is 9T

unessential – U, very low – VL, fairly low – FL, low – Lmedium – M, high – H, medium high – MH, very high –VH and perfect – P. Linguistic descriptors have thefollowing values Figure 3.

0, 0

(0.125 ) / 0.125 0 0.125U l

x

x x

(14)

/ 0.125, 0 0.125

(0.250 ) / 0.125, 0.125 0.25VLl

x x

x x

(15)

( 0.125) / 0.125, 0.125 0.250

(0.375 ) / 0.125 0.250 0.375 FLl

x x

x x

(16)

( 0.50) / 0.125, 0.50 0.625

(0.75 ) / 0.125 0.625 0.75 H l

x x

x x

(17

( 0.375) / 0.125, 0.375 0.50

(0.625 ) / 0.125 0.50 0.625 M l

x x

x x

(18)

( 0.50)/ 0.125, 0.50 0.625

(0.75 )/ 0.125 0.625 0.75 H l

x x

x x

(19)

( 0.625) /0.125, 0.625 0.75(0.875 ) /0.125 0.75 0.875 MH l x x

x x

(20)

( 0.75) /0.125, 0.75 0.875

(1 ) / 0.125 0.875 1VH l

x x

x x

(21)

( 0.875) / 0.125, 0.875 1

1, 1 P l

x x

x

(22)




D e t e r m i n i n g t h e b e s t

a l t e r n a t i v e

S t r e n g t h s ( S )

W e a k n e s s e s

( W )

O p p u r t u n i t i e s ( O )

T h r e a t s ( T

)

C a p a b l e a n d c o m p e t e n t p e r s o n n e l ( S 1 )

T a c t i c a l - o p e r a t i o n a l u n i t s s w i f t d i s l o c a t i o n

c a p a b i l i t y ( S 2 )

S t r o n g m a n a g e

m e n t t e a m ( S 3 )

L a r g e n u m b e r o f h i e r a r c h i c a l l e v e l s ( W 1 )

W e a k p e r s o n n e l m o t i v a t i o n p o s s i b i l i t i e s ( W 2 )

I n s u f f i c i e n t o r g a n i s a t i o n a l s t r u c t u r e e f f i c i e n c y ( W 3 )

B a d c o o r d i n a t i o n ( W 4 )

I n s u f f i c i e n t e x p

e r i e n c e s h a r i n g w i t h f o r e i g n a r m e d

f o r c e s ( W 5 )

P a r t i a l o p t i m i s a

t i o n ( W 6 )

P o o r r e s o u r c e s

e x p l o i t a t i o n ( W 7 )

B e t t e r c o o p e r a

t i o n w i t h f o r e i g n a r m e d f o r c e s ( O 1 )

L i b e r a l i s a t i o n o

f p e r s o n n e l e d u c a t i o n a b r o a d ( O 2 )

M o d e r n i n f o r m a t i o n a l t e c h n o l o g i e s d e v e l o p m e n t i n

t h e a r e a o f b u s

i n e s s o r g a n i s a t i o n ( O 3 )

E s t a b l i s h i n g o f

l o g i s t i c s u p p o r t o r g a n i s a t i o n c a p a b l e

o f s a t i s f y i n g c o

m m a n d d e m a n d s ( O 4 )

G r o u p i n g o f o r g a n i s a t i o n a l u n i t s a c c o r d i n g t o

N A T O s t a n d a r d s ( O 5 )

M i n i m u m n u m b

e r o f h i e r a r c h i c a l l e v e l s ( O 6 )

P o l i t i c a l a n d e c

o n o m i c i n s t a b i l i t y i n S e r b i a ( T 1 )

Q u a l i f i e d p e r s o

n n e l o u t f l o w ( T 2 )

C h a n g e s i n l o g

i s t i c s u p p o r t d o c t r i n e ( T 3 )

C h a n g e s i n t h e

c o u n t r y ’ s d e f e n c e d o c t r i n e ( T 4 )

A l t e r n a t i v e 1




Figure 3. FMM model for SWOT.

To determine the relative importance of the evaluationcriteria SWOT, they were pair-wise compared with

respect to the goal by using the fuzzyfied. In Table 1, theevaluation of linguistic criterions for each of the presented



Pamucar et al. 5383

Table 1. Optimality criterion level of influence on the observed alternatives.

Criteria and sub-criteriaLinguistic criteria Benefit-cost criteria

A1 A2 A3 A4 Min Max

Strengths

Capable and competent personnel M MH H H

Tactical-operational units swift dislocation capability M VH H MH

Strong management team M VH H MH

Weaknesses

Number of hierarchical levels H M M M

Personnel motivation possibilities L VH H H

Organisational structure efficiency L VH M MH

Coordination VL VH M VH

Sharing experience with foreign armed forces VL VH M P

Partial optimisation VH VL L FL

Resources exploitation M VH H VH

Opportunities

Cooperation with foreign armed forces L VH MH VH

Liberalisation of personnel education abroad M VH MH VH

Modern informational technologies introduction in the area of business organisation L VH M VH

Establishing of logistic support organisation capable of satisfying command demands VL VH M H

Grouping of organisational units according to NATO standards L H M VH

Participation in logistic support of the NATO forces VL MH M VH

ThreatsPolitical and economic instability in Serbia VH M VH H

Qualified personnel outflow VH MH VH MH

Changes in logistic support doctrine VH M H H

Changes in the country’s defence doctrine VH M H H

Figure 4. Linguistic descriptors.

alternatives according to observed optimality criterionsare given. Linguistically expressed preferences among

criteria have been used to create a judgment matrix W as

given in step 4. Following the decision-maker’s criterion

assessment, normalisation of optimality criteria usingEquations 1 and 2 is performed. The weighting vector

kij

w of criteria matrix W was determined by applying

Equation 6. Each entry of this vector is the sum ofelements in the related row of matrix W and divided by

the sum of all its elements.

(0.32,0.30,0.27) 0.33

(0.40,0.36,0.32) 0.29

(0.16,0.18,0.21) 0.20

(0.12,0.15,0.20) 0.17

s

w

SWOT

o

t

w

wW

w

w



Pamucar et al. 5385

Тable 3. Additive synthesis.

SWOT factors Alternative 1 Alternative 2 Alternative 3 Alternative 4 W2 W1

Strengths

S1 (0.119,0.113,0.109) (0.119,0.113,0.109) (0.078,0.084,0.088) (0.078,0.084,0.088) 0.390.33

S2 (0.129,0.103,0.092) (0.129,0.103,0.092) (0.000,0.026,0.037) (0.000,0.026,0.037) 0.26

S3 (0.116,0.108,0.102) (0.116,0.108,0.102) (0.077,0.080,0.083) (0.040,0.053,0.062) 0.35

Weaknesses

W1 (0.027,0.028,0.030) (0.027,0.028,0.030) (0.018,0.021,0.024) (0.046,0.042,0.036) 0.12

0.29

W2 (0.030,0.031,0.032) (0.045,0.042,0.039) (0.030,0.031,0.032) (0.030,0.031,0.032) 0.13

W3 (0.024,0.027,0.030) (0.036,0.036,0.037) (0.024,0.027,0.030) (0.060,0.053,0.045) 0.14

W4 (0.016,0.022,0.028) (0.046,0.045,0.046) (0.030,0.033,0.037) (0.076,0.067,0.056) 0.17

W5 (0.028,0.027,0.027) (0.028,0.027,0.027) (0.018,0.020,0.022) (0.028,0.027,0.027) 0.10

W6 (0.040,0.040,0.040) (0.040,0.040,0.040) (0.040,0.040,0.040) (0.040,0.040,0.040) 0.16

W7 (0.025,0.029,0.035) (0.063,0.058,0.052) (0.025,0.029,0.035) (0.063,0.058,0.052) 0.18

Opportunities

O1 (0.017,0.021,0.027) (0.043,0.042,0.040) (0.043,0.042,0.040) (0.043,0.042,0.040) 0.15

0.20

O2 (0.023,0.028,0.034) (0.058,0.055,0.050) (0.058,0.055,0.050) (0.035,0.037,0.042) 0.18

O3 (0.012,0.014,0.017) (0.031,0.029,0.026) (0.031,0.029,0.026) (0.012,0.014,0.017) 0.09

O4 (0.023,0.028,0.036) (0.058,0.056,0.054) (0.058,0.056,0.054) (0.058,0.056,0.054) 0.20O5 (0.018,0.021,0.025) (0.046,0.042,0.037) (0.009,0.014,0.019) (0.046,0.042,0.037) 0.12

O6 (0.014,0.017,0.022) (0.035,0.034,0.032) (0.035,0.034,0.032) (0.035,0.034,0.032) 0.12

Threats

T1 (0.050,0.059,0.071) (0.127,0.118,0.106) (0.050,0.059,0.071) (0.127,0.118,0.106) 0.35

0.17T2 (0.009,0.011,0.013) (0.022,0.021,0.019) (0.013,0.014,0.016) (0.022,0.021,0.019) 0.07

T3 (0.076,0.076,0.076) (0.076,0.076,0.076) (0.076,0.076,0.076) (0.076,0.076,0.076) 0.30

T4 (0.069,0.069,0.069) (0.069,0.069,0.069) (0.069,0.069,0.069) (0.069,0.069,0.069) 0.27

Table 4. Final ranking of alternatives.

Decision alternative

Index of optimism

Final rankλ = 0.0 (pessimistic) λ = 0.5 (moderate) Λ = 1.0 (optimistic) Alternative 1 0.205 0.212 0.220 4

Alternative 2 0.285 0.295 0.305 1

Alternative 3 0.210 0.220 0.230 3

Alternative 4 0.245 0.255 0.265 2

relevant to the design of organisations as well as theirinfluence on the choice of alternatives have their valuesdisplayed as numerical values or fuzzy linguisticdescriptors. Since the process of organisational designoften involved a number of experts, the model allows fora possibility of optimality criteria values synthesis in caseof group decision-making. Decision-making in a groupdiffers from individual decision-making on methodologicaland mathematical levels. Group syntheses with completeand incomplete information are discussed in the model.In addition, the model enables comparison of the criterionfunctions output values using two methods namely:dephasification of the centre of gravity and the totalintegral value method. Application of the given model isshown on the example of designing the organisationalstructure of the governing bodies of transport support.

The complex environment, in which these governingbodies act, does not tolerate organisational improvisationrather requires a planned and methodologicaorganisational project and its constant modification andadaptation.

Selection of the appropriate organisational structure isone of the most significant decisions, as the capabilitiesof the governing system will be significantly slowed downif an organisational structure is inadequate for thecircumstances in which the organisation is. Although themodel application was shown on the example ofdesigning governing bodies within the armed forces, itpossesses great flexibility and can be adapted to anyparticular problem. Very easily, with minor modificationsit can be applied for the selection of organisationastructure of any business system.




REFERENCES

Bender MJ, Simonovic SP (2000). A fuzzy compromise approach to

water resources systems planning under uncertainty. Fuzzy Set.Syst., 115: 35-44.

Bozanic D, Pamucar D (2010). Evaluating locations for river crossing

using fuzzy logic. Milit. Tech. Cour., 1: 129-145.Brans JP, Vincke P, Mareschal B (1986). How to select and how to rank

projects by the Promethee method. Eur. J. Oper. Res., 24: 228-238.Deng H (1999). Multicriteria analysis with fuzzy pairwisecomparison. Int.

J. Approx. Reason., 21: 215-231.Hwang CL, Yoon KS (1981). Multiple attribute decision making:

methods and applications. Springer, Berlin.Kujacic M, Bojovic N (2003). Organizational design of post corporation

structure using fuzzy multicriteria decision making. Comput. Math.

Organ. Theory, 9: 5-18.Liou TS, Wang MJJ (1992). Ranking fuzzy numbers with integral value.

Fuzzy Set. Syst., 50: 247-256.

Pamucar D (2009). Design of the organisational structure using fuzzylogic approach. Master paper. Serbia: Faculty of Transport andTraffic Engineering, Belgrade.

Pamucar D (2010). Using fuzzy logic and neural networks duringdecision making proces in transport. Milit. Techn. Cour., 3: 125-143.

Pamucar D, Bozanic D, Dorovic B, Milic A (2011). Modelling of the fuzzylogical system for offering support in making decisions within theengineering units of the Serbian army. Int. J. Phys. Sci., 3: 592-609.

Roy B (1968). Ranking and selection in the presence of multipleviewpoints. Comput. Oper. Res., 8: 57-75.

Saaty TL (1980). The analytic hierarchy process. McGraw-Hill, New

York.Srdevic B, Medeiros Y, Srdevic Z, Schaer M (2002). Evaluating

management strategies in Paraguacu river basin by analytichierarchy process. First Biennial Meeting Int. Environ. ModelingSoftware Soc., 1: 42-47.

Triantaphyllou E, Lin CT (1996). Development and evaluation of five

multiattribute decision making methods. Int. J. Approx. Reason., 14281-310.

Zadeh LA (1965). Fuzzy sets. Inf. Control. 8: 338-353.

Zeleny M (1982). Multiple citeria decision making. McGraw-Hill BookCompany, New York.

organisational design of the management of the traffic support using fuzzy multi criteria decision...

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