Page - 194 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 270 Then,accordingtoTable4andEquations (9)and(10), the initial fuzzydecisionmatrix rD canbe obtained,asbelow: rD“ »——————————————————————————————————– C1 C2 C3 C4 C5¨˚ ˚˚˚˚ ˝ 0.50 0.30 0.21 0.43 0.27 0.20 0.75 0.38 0.25 0.25 0.19 0.17 1.00 0.50 0.30 ‹˛‹‹‹‹‚ ¨˚ ˚˚˚˚ ˝ 0.38 0.59 0.81 0.27 0.49 0.70 0.70 0.89 1.00 0.24 0.43 0.65 0.38 0.59 0.78 ‹˛‹‹‹‹‚ ¨˚ ˚˚˚˚ ˝ 0.29 0.18 0.14 0.50 0.25 0.17 1.00 0.40 0.22 0.20 0.14 0.11 0.25 0.17 0.13 ‹˛‹‹‹‹‚ ¨˚ ˚˚˚˚ ˝ 0.23 0.46 0.69 0.34 0.57 0.80 0.57 0.80 1.00 0.29 0.51 0.74 0.51 0.74 0.97 ‹˛‹‹‹‹‚ ¨˚ ˚˚˚˚ ˝ 0.33 0.55 0.79 0.30 0.55 0.79 0.55 0.79 1.00 0.24 0.48 0.73 0.48 0.73 0.94 ‹˛‹‹‹‹‚ C6 C7 C8 C9 C10¨˚ ˚˚˚˚ ˝ 0.26 0.46 0.69 0.29 0.51 0.74 0.63 0.83 1.00 0.29 0.51 0.74 0.51 0.74 0.94 ‹˛‹‹‹‹‚ ¨˚ ˚˚˚˚ ˝ 0.44 0.67 0.86 0.33 0.56 0.78 0.61 0.83 1.00 0.11 0.28 0.50 0.36 0.56 0.75 ‹˛‹‹‹‹‚ ¨˚ ˚˚˚˚ ˝ 0.17 0.10 0.07 0.20 0.11 0.08 1.00 0.29 0.14 0.14 0.09 0.07 0.20 0.11 0.08 ‹˛‹‹‹‹‚ ¨˚ ˚˚˚˚ ˝ 0.21 0.42 0.63 0.42 0.63 0.84 0.68 0.87 1.00 0.11 0.24 0.42 0.47 0.68 0.87 ‹˛‹‹‹‹‚ ¨˚ ˚˚˚˚ ˝ 0.51 0.72 0.90 0.36 0.56 0.77 0.67 0.87 1.00 0.26 0.46 0.67 0.62 0.82 0.97 ‹˛‹‹‹‹‚ C11 C12 C13¨˚ ˚˚˚˚ ˝ 0.06 0.23 0.46 0.34 0.57 0.80 0.63 0.83 0.97 0.14 0.34 0.57 0.57 0.80 1.00 ‹˛‹‹‹‹‚ ¨˚ ˚˚˚˚ ˝ 0.11 0.08 0.06 0.14 0.09 0.07 1.00 0.25 0.13 0.08 0.06 0.05 1.00 0.25 0.13 ‹˛‹‹‹‹‚ ¨˚ ˚˚˚˚ ˝ 0.23 0.17 0.14 0.50 0.28 0.19 1.00 0.42 0.25 0.25 0.18 0.14 1.00 0.42 0.25 ‹˛‹‹‹‹‚ fiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifl AccordingtoTable4,Equations(20)and(21), thesubjectiveweightsofsub-criteriacanbeobtained. Ontheotherside, theobjectiveweightsofsub-criteriacanalsobeobtainedbyfuzzydecisionmatrix rD andEquations (21)–(26). Finally, thecombinationweightsofall sub-criteriaequal to theaverageof subjectiveandobjectivesub-criteriaweights,whichareshowninTable6, canbeobtainedthatC2,C4, C5,C6,C7,C10,C11arebenefitsub-criteriaandC1,C3,C8,C9,C12,C13arecost sub-criteria. Table6.Combinationweightsofevaluationcriteria. C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 wsubjective0.0853 0.1109 0.0603 0.0686 0.0763 0.0686 0.0429 0.0769 0.1109 0.1282 0.0513 0.0429 0.0769 wobjective 0.0832 0.0845 0.0764 0.0769 0.0787 0.0795 0.0798 0.0681 0.0787 0.0728 0.0689 0.0781 0.0743 wj 0.0842 0.0977 0.0683 0.0727 0.0775 0.0741 0.0614 0.0725 0.0948 0.1005 0.0601 0.0605 0.0756 ThenormalizedfuzzydecisionmatrixcanbeobtainedbasedonEquations (11)and(12). Then thedistances of alternatives from thepositive ideal solutions andnegative ideal solutions canbe calculatedaccordingtoEquations (6)and(16)–(18). Finally, compute thevaluesofQi forfiveEVCS sitealternativesaccordingtoEquation(13).Andthusrankanddeterminetheoptimalsite forEVCS basedontheprincipleofVIKOR.TheresultsareshowninTable7. Table7.ThevaluesofSi,Ri andQi foreachalternative. A1 A2 A3 A4 A5 Si 0.512 0.532 0.972 0.443 0.759 Ri 0.070 0.066 0.049 0.084 0.064 Qi 0.733 0.655 0.000 1.000 0.408 Rank 4 3 1 5 2 Obviously,EVCSsitealternativeA3outranksother fouralternatives. Therefore,A3,namely the EVCSsite inNankaidistrictofTianjinshouldbeselectedas theoptimalEVCSsite. 7.Discussion TheEVCSsitealternativesarerankedbyusingFDM,combinationweightsandfuzzyGRA-VIKOR methods. Basedon theQi, the rankingof all EVCSselections indescendingorder areA3,A5,A2, A1andA4. Thebest alternative is foundtobeA3, and thesecondbest alternative isA5. Basedon aboveresults, thisproposedmodelcaneasilyevaluateandselectabestalternative. In this section, to 194