Page - 185 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 270 Table1.Fuzzyevaluationscores for thealternatives. LinguisticTerms FuzzyScore Verypoor (0,0,1) Poor (0,1,3) Mediumpoor (1,3,5) Fair (3,5,7) Mediumgood (5,7,9) Good (7,9,10) Verygood (9,10,10) Step1.Calculate theaggregatedfuzzy linguistic ratings forcriteriaperformanceofalternatives. Suppose that therearemalternativesA={A1,A2, . . . Am} tobeevaluated. Theperformanceofn criteriaareby linguistic termswhichareobtainedfrom rdecisionmakers. Let rxijk “ ´xLijk,xMijk ,xUijk¯, 0 ď xLijk ď xMijk ď xUijk ď 1, i “ 1,2, ¨¨¨m, j “ 1,2, ¨¨¨n,k “ 1,2, ¨¨¨ rbe the linguistic ratingon theperformance criteriaCj respect toalternativeAi byexpertEk. Then the aggregatedfuzzy linguistic ratingrxij “´xLij,xMij ,xUij ¯canbeobtainedas follows: rxij “´xLij,xMij ,xUij ¯“ ˜ rÿ k“1 xL ijk r , rÿ k“1 xM ijk r , rÿ k“1 xU ijk r ¸ (9) Step2.Assemble the initial fuzzydecisionmatrix. According to Equation (9), the initial fuzzy decisionmatrix rD can be obtained, as shown in Equation(10).AMCDMproblemcanbeexpressedconcisely in the formof triangular fuzzynumber, as follows: rD“ `rxij˘mˆn “ »————– rx11 rx12 ¨¨¨ rx1nrx21 rx22 ¨¨¨ rx2n ... ... ... ...rxm1 rxm2 ¨¨¨ rxmn fiffiffiffiffifl“ »————– pxL 11 ,xM 11 ,xU 11 q pxL 12 ,xM 12 ,xU 12 q ¨¨¨ pxL 1n ,xM 1n ,xU 1n q pxL 21 ,xM 21 ,xU 21 q pxL 22 ,xM 22 ,xU 22 q ¨¨¨ pxL 2n ,xM 2n ,xU 2n q ... ... ¨¨¨ ... pxL m1 ,xM n1 ,xU n1 q pxL m2 ,xM m2 ,xU m2 q ¨¨¨ pxLmn,xMmn,xUmnq fiffiffiffiffifl (10) Step3.Normalize the initial fuzzydecisionmatrixusing linearscale transformation. Toensure thecompatibilityamongevaluationcriteria, the initial fuzzydecisionmatrixshouldbe transformedintoacomparablescale. Thenormalizedfuzzydecisionmatrix isdenotedby rR [50]: rR“ “rij‰mˆn For thebenefitcriteria: rij “pxLiju`ij , xM 12 u`ij , xU 12 u`ij qandu`ij “maxixUij (11) For thecostcriteria: rij “pu´ijxLij , u´ij xMij , u´ij xUij qandu´ij “minixLij (12) Step4.Definethereferentialsequencesoffuzzypositiveidealsolutionandnegativeidealsolution. The referential sequences of positive ideal solutionA+ andnegative ideal solutionA– canbe determinedas follows: A` “ “r`01,r`02,¨¨¨r`0n‰ ,A´ “ “r´01,r´02,¨¨¨r´0n‰ (13) where r`0j “maxi `rij˘, r´0j “mini `rij˘, j=1,2, . . . n 185