对方案有偏好的三角模糊数型多属性决策方法研究

248SystemsEngineeringandElectronicsVol124,No182002:2001-05-23:2001-09-15:(79970093):(1968-),,,,:1001O506X(2002)08O0009O04(,210096)::;;,,,,:;;;:C934:AStudyonMethodforTriangularFuzzyNumber2BasedMulti2AttributeDecisionMakingWithPreferenceInformationonAlternativesXUZe2shui(SchoolofEconomicsandManagement,SoutheastUniversity,Nanjing210096,China)Abstract:Westudythemulti2attributedecision2makingproblem,inwhichtheattributeweightinformationisincomplete,andtheelementsindecision2makingmatrixandsubjectivepreferencevaluesaretriangularfuzzynumbers,andproposeasimilaritydegree2basedmethodfortriangularfuzzynumber2basedmulti2attributedecisionmakingwithpreferenceinformationonalternatives1Byusingthismethod,alinearprogrammingmodelisestablishedfirstly,andtheattributeweightsarederivedbysolvingthismodel,then,basedonapossibilitydegreeformulaforcomparingtwotriangularfuzzynumbersandaformulaforprioritiesofcomplementaryjudge2mentmatrix,aprioritymethodforalternativesispresented1Finally,anumericalexampleisgiven.Keywords:Triangularfuzzynumber;Weight;Model;Multi2attributedecision2making1,[1,2],:[35]:,,,,[69],,,,,,,21a=(aL,aM,aU),0aLaMaU,a,()[10]a(x)=(x-aL)/(aM-aL)aLxaM(x-aU)/(aM-aU)aMxaU02a=(aL,aM,aU),b=(bL,bM,bU),s(a,b)=aLbL+aMbM+aUbUmax(aL)2+(aM)2+(aU)2,(bL)2+(bM)2+(bU)2(1)a,b,s(a,b)=min(aL)2+(aM)2+(aU)2,(bL)2+(bM)2+(bU)2aLbL+aMbM+aUbU(2)a,b,s(a,b),a,b,s(a,b)=1,a=b,a,b,a=(aL,aM,aU),b=(bL,bM,bU),(1)a+b=(aL,aM,aU)+(bL,bM,bU)=(aL+bL,aM+bM,aU+bU)(2)1a=1aU,1aM,1aL3a=(aL,aM,aU),b=(bL,bM,bU),p(ab)=min{aM-aL+bM-bL,max(aM-bL,0)}aM-aL+bM-bL+(1-)max{aU-aM+bU-bM,max(aU-bM,0)}aU-aM+bU-bM(3)ab,p(ba)=max{aM-aL+bM-bL,max(bM-aL,0)}aM-aL+bM-bL+(1-)max{aU-aM+bU-bM,max(bU-aM,0)}aU-aM+bU-bM(4)ba015,;=015,;015,(1)=1,p(ab)ab;(2)=0,p(ab)ab,1a=(aL,aM,aU),b=(bL,bM,bU),(1)0p(ab)1,0p(ba)1;(2)bual,p(ab)=1,aubl,p(ba)=1;(3)aubl,p(ab)=0,bual,p(ba)=0;(4)p(aa)=12;(5)p(ab)+p(ba)=1X={x1,x2,,xn},U={u1,u2,,um},w=(w1,w2,,wm)T,H,,H,xjX,vj(vj=(vLj,vMj,vUj),0vLjvMjvUj1,,)xjX,iui,xjuiaij(aij=aLij,aMij,aUij),A=(aij)mn;Ii(i=1,2),M={1,2,,m},N={1,2,,n},,A=(aij)mnR=(rij)mn,rij=(rLij,rMij,rUij),rij=aij/ai,iI1,jN(5)rij=(1/aij)/(1/ai),iI2,jN(6)ai=nj=1a2ij,1/ai=nj=1(1/aij)2,(5)(6)rLij=aLij/nj=1(aUij)2rMij=aMij/nj=1(aMij)2,iI1,jNrUij=aUij/nj=1(aLij)2(7)rLij=(1/aUij)/nj=1(1/aLij)2rMij=(1/aMij)/nj=1(1/aMij)2,iI2,jNrUij=(1/aLij)/nj=1(1/aUij)2(8)rijuixj,,,w()R=(rij)mn,2,(SOM)maxF(w)=mi=1nj=1s(rij,vj)wis.t.w=(w1,w2,,wm)TH,wi0,mi=1wi=1s(rij,vj)(1)(2),ijvj()rij,wii,F(w)012002(),w:,,w=(w1,w2,,wm)T,zj=mi=1rijwi,jN(9)zj(jN),,(3)(4),zj(jN),P=(pij)nn,pij=P(zizj),[11]=(1,2,,n)Ti=nj=1Pij+n2-1n(n-1),iN(10)P,,,(1),X={x1,x2,,xn},U={u1,u2,,um}xjiaij(aij=(aLij,aMij,aUij)),A=(aij)mnxjX,vj(vj=(vLj,vMj,vUj),0vLjvMjvUj1);(2)A=(aij)mn(7),(8)R=(rij)mn;(3)(SOM)w,(9)zj(jN);(4)(3)(4),pij=P(zizj),P=(pij)nn;(5)(10)P=(1,2,,n)T,;(6)4,;,,6():(1)(2)(3)(4)(5)(6),,,,5xj(j=1,2,3,4,5)(),()11x1x2x3x4x51[0180,0185,0190][0190,0195,1100][0188,0191,0195][0185,0187,0190][0186,0189,0195]2[0190,0192,0195][0189,0190,0193][0184,0186,0190][0191,0193,0195][0190,0192,0195]3[0191,0194,0195][0190,0192,0195][0191,0194,0197][0185,0188,0190][0190,0195,0197]4[0193,0196,0199][0190,0192,0195][0191,0194,0196][0186,0189,0193][0191,0193,0195]5[0190,0191,0192][0194,0197,0198][0186,0189,0192][0187,0190,0194][0190,0192,0196]6[0195,0197,0199][0190,0193,0195][0191,0192,0194][0192,0193,0196][0185,0187,0190]H={0115w1012,0110w2012,0116w3012,0105w4011,0118w5012,0119w60130}51118A=[0180,0185,0190][0190,0195,1100][0188,0191,0195][0185,0187,0190][0186,0189,0195][0190,0192,0195][0189,0190,0193][0184,0186,0190][0191,0193,0195][0190,0192,0195][0191,0194,0195][0190,0192,0195][0191,0194,0197][0185,0188,0190][0190,0195,0197][0193,0196,0199][0190,0192,0195][0191,0194,0196][0186,0189,0193][0191,0193,0195][0190,0191,0192][0194,0197,0198][0186,0189,0192][0187,0190,0194][0190,0192,0196][0195,0197,0199][0190,0193,0195][0191,0192,0194][0192,0193,0196][0185,0187,0190],(7)AR=[0134,0137,0141][0138,0142,0145][0138,0141,0144][0137,0139,0142][0137,0140,0144][0139,0141,0143][0138,0139,0142][0136,0139,0142][0140,0142,0144][0139,0141,0144][0139,0141,0143][0138,0140,0143][0140,0142,0145][0137,0140,0142][0139,0142,0145][0140,0142,0145][0138,0140,0143][0140,0142,0144][0138,0140,0143][0139,0142,0144][0139,0140,0142][0140,0142,0144][0137,0140,0142][0138,0141,0144][0139,0141,0144][0141,0143,0145][0138,0141,0143][0140,0141,0143][0140,0142,0145][0137,0139,0141]5xj(j=1,2,3,4,5)v1=[0130,0135,0140],v2=[0135,0140,0145]v3=[0135,0140,0150],v4=[0140,0145,0155]v5=[0140,0150,0160](1)(),22s(ri1,v1)s(ri2,v2)s(ri3,v3)s(ri4,v4)s(ri5,v5)u10194001962019710183401795u20185601986019240188901812u30185601994019890184101826u40183001994019960185501818u50187001996019380187001812u60181601986019750189701765SOMmaxF(w)=41502w1+41467w2+41506w3+41493w4+41486w5+41439w6s1t10115w10125,0110w20120116w30122,0105w401150118w50125,0119w60130wi0,6i=1wi=1w=(0125,0110,0122,0106,0118,0119)T(9)5z1=(01382,01403,01428),z2=(01384,01410,01436)z3=(01386,01409,01435),z4=(01381,01405,01432)z5=(01381,01407,01437),(3)zj(j=1,2,,5)(,=015)P=015