Page - 186 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 270 Step5:Compute thedistancesofeachalternative fromthepositive ideal solutionandnegative ideal solution[51]. rSi “ nÿ j“1 wj ˜r`0j´rijr`0j´r´0j ¸ (14) rRi “max j « wj ˜r`0j´rijr`0j´r´0j ¸ff (15) i“1,2¨¨¨m, j“1,2¨¨¨n wherewj represents theweightof criteriaCj, rSidenotes thedistance rateofAi to thepositive ideal solutionA+,and rRidenotes thedistancerateofAi to thenegative ideal solutionA–. Inorder tobetter reflectdistanceof eachalternative to thepositive andnegative idealpoints, the fuzzygreyrelationcoefficient (FGRC) is introducedtomodify theconventional formulaof fuzzy VIKOR,whichareshownas follows[16]: γ ´ru0j,rij¯ ,u“`,´ γ ´ru0j,rij¯“ miniminjrduij`ξmaximaxjrduijrduij`ξmaximaxjrduij “ miniminjrd´ru0j,rij¯`ξmaximaxjrd´ru0j,rij¯rd´ru0j,rij¯`ξmaximaxjrd´ru0j,rij¯ (16) rSi “ nÿ j“1 wjγ ´r`0j,rij¯ (17) rRi “max j wjγ ´r´0j,rij¯ (18) Step6:Compute thevalueofQi foreachalternativeasbelow: Qi “ν Si´S ` S´´S` `p1´νq Ri´R` R´´R` (19) whereS+=maxiSi,S– =miniSi,R+=maxiRi,R– =miniRi, andv is theweightof thestrategyof“the maximumgrouputility”,whereas (1–v) represents theweightof the individual regret. Step7:Rankthealternativesaccordingto thevalueofQi inStep5. Onthebasisof theconceptsofGRAandfuzzyVIKORmethod,all alternativescanberankedby thevalueofQi. Obviously, for thealternativeAiwhich iscloser to thepositive idealpointandfarther fromthenegative idealpoint, thevalueofQi iszero. Inaddition,onlywhenthealternativewhich is thebest rankedbythevalueofQi satisfies the followingconditions, it canbeselectedas theoptimalsolution. (I) Acceptableadvantage: Q ´ Ap2q´Ap1q ¯ ěDQ whereA(2) is the second in the list of priorities byQi; DQ = 1/(N–1), N is the number of alternatives [51]. (II) Acceptablestability indecision-making: ThealternativeA(1)mustalsobe thebest rankedby rSiorRi. Thiscompromisesolution isstable within thedecision-makingprocess,whichcouldbe thestrategyofmaximumgrouputility (when v>0.5 isneeded),or“byconsensus” (v«0.5),or“withveto” (v<0.5). Ifoneof theconditions isnot satisfied, thenthesetof solutions isproposed[16],whichconsistsof: A(1) andA(2), ifonly thecondition(II) isnotsatisfied,or 186