一种新的模糊群体决策方法

200177:100026788(2001)0720081206,,(,100083):,,L,,,L:;;:C94:AaANewApproachofGroupDecisionMakingunderFuzzyPreferenceWEICun2ping,QIUWan2hua,WANGXin2zhe(SchoolofManagement,BeijingUniversityofAeronauticsandAstronautics,Beijing100083,China)AbstractBasedonthesimilaritymeasuringfunction,anewsimilaritymeasuringfunctionisdefined.Anewfuzzygroupdecisionmakingmethodisproposed,whichconstructstrapezoidalfuzzynumberstorepresentthesubjectiveestimateofalternativesandrankingthetrapezoidalfuzzynumbers.Finally,anumericalexampleisgiven.Keywordstrapezoidalfuzzynumber;similaritymeasuringfunction;groupdecisionmaking1,L[16]LTanino,[2]LNurmi[3]LHsu,[1]L,[4],[5]L,L2,L,,La:1999209202©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.2.11R,R(R)RZAR(R),:1)A,x0R,LA(x0)=1;2)A,LA(Kx+(1-K)y)Emin(LA(x),LA(y))Z2A,fA:R[0,1]:fA=(x-c)ö(a-c),cFxFa1,aFxFb(x-d)ö(b-d),bFxFd0,with-aFbFcFd(c,a,b,d),Z3A=(c,a,b,d)EV(A)=12[E-(A)+E+(A)],E-(A)=12(c+a),E+(A)=12(b+d)Z2.2,nmZ,,,Z,[5]Z,ijxij,fxij(x),ijZE={e1,e2,,en},A={a1,a2,,am},nmM:M=x11x12x1mx21x22x11xn1xn2xnmHsu[1],,Z,,Z,,ZHsu(consensusoragreement),Z,[7]Z,,,Z2.3:ZZ4wi=(ci,ai,bi,di),wj=(cj,aj,bj,dj),2820017©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.s(wi,wj)=EViEVj,EViFEVjEVjEVi,EVjFEVi,EViEVjwi,wjZ[1]ij,,Z4,Z1wi,wj,0Fs(wi,wj)F1;s(wi,wj)=1EViEVj;s(wi,wj)=0EViEVj0,0,0,(crisp)0Z14Z,M:M=1s12s1ns211s2nwsn1sn21,sij=s(wi,wj),i=j,sij=1,ei:A(ei)=1n-16nj=1jisij,ei:RADi=A(ei)6ni=1A(ei)Mn,m,Z2.4,Zj,:xgj=f(x1j,x2j,,xnj)=6ni=1wiáxij,j=1,,m,,:,ZDelphi,Z5Z5,wi=AEIDi+(1-A)RADi,i=1,,n;,A,0FAF1,wi;EIDii,6iEIDi=1,0FEIDiF1;RADii,6iRADi=1,0FRADiF1ZAEIDiRADiwi,Z2.5j,:2[8]Zxijij,i,k387©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.xij=xkj,xgj=xijZ,j,jZjxgjj,xgj=6ni=1(wiáxij)=xijá6ni=1wi=xijá6ni=1[AõEIDi+(1-A)3RADi]=xijáA36ni=1EIDi+(1-A)36ni=1RADi=xijá[A+(1-A)]=xij3[8]Zxgj=f(x1j,x2j,,xnj)=f(x(1)j,x(2)j,,x(n)j)xgj=f(x1j,x2j,,xnj)=6ni=1wiáxij,j=1,,m,,Z23Z4ZL,,f(L(x1j),L(x2j),,L(xnj))=L(f(x1j,x2j,,xnj)).L,Z2.6,Z,Z[913],[1011]{xg1,xg2,,ggm}Z2.6.16Smax={(x,fsmax(x))ûxR},fsmax=(x-x1)ö(x2-x1),x1FxFx20R,x1=minj{cgj},x2=maxj{dgj},j=1,,m,xgj=(cgj,agj,bgj,dgj)Z7Smin={(x,fsmin(x))ûxR},fsmin=(x-x1)ö(x1-x2),x1FxFx20R,x1=minj{cgj},x2=maxj{dgj},j=1,,m,xgj=(cgj,agj,bgj,dgj)Z2.6.28jUsmax(j)=supx(fsmax(x)fxgj(x)),j=1,,m,fxgj(x)xgjZ9jUsmin(j)=1-supx(fsmin(x)fxgj(x)),j=1,,m,fxgj(x)xgjZ10j4820017©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.UT(j)=AUsmax(j)+(1-A)Usmin(j),,j=1,,m,0FAF1,A,ZA0.5,;A0.5,;A=0.5,Z11ij,aiaj,UT(i)UT(j),UT(i)=UT(j),EViEVjZ12ij,ai=aj,UT(i)=UT(j),EVi=EVjZ3:E={e1,e2,e3},A={a1,a2,a3},:x11=(0.2,0.25,0.27,0.3)x12=(0.4,0.43,0.45,0.5)x13=(0.7,0.74,0.78,0.8)x21=(0.28,0.3,0.35,0.4)x21=(0.3,0.36,0.38,0.4)x23=(0.5,0.55,0.6,0.65)x31=(0.35,0.4,0.42,0.45)x32=(0.45,0.49,0.52,0.55)x33=(0.55,0.6,0.65,0.7):EID=(0.3,0.5,0.2),:RAD=(0.327,0.337,0.336),:w=(0.31,0.42,0.27),A=0.5,,:xg1=(0.2734,0.3107,0.3433,0.3816)xg2=(0.3706,0.4158,0.4385,0.4704)xg3=(0.5744,0.6212,0.6680,0.7086)x1=mini{cgi}=0.2743,x2=maxi{dgi}=0.7086,i=1,2,3,Usmax(1)=0.227,Usmax(2)=0.4204,Usmax(3)=0.9146,Usmin(1)=0.0792,Usmin(2)=0.2952,Usmin(3)=0.7212,UT(j)=AUsmax(j)+(1-A)Usmin(j)A=0.5,UT(1)=0.153,UT(2)=0.3578,UT(3)=0.8179,:UT(1)UT(2)UT(3)3Z4[1],L,L,,L:1),,,,;2),EIDiRADi,,L3),L4)L587©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.:[1]HsuHsimei,ChenChentung.Aggregationoffuzzyopinionundergroupdecisionmaking[J].FuzzySetsandSystems.1996;79(3):279-285.[2]TaninoT.OnGroupdecisionmakingunderfuzzypreferences[A].In:JKacprzyk,MFeddrizziEds.MultipersonDecisionMakingUsingFuzzySetsandPossibilityTheory[C].Dordrecht;Boston,KlumerAeademicPublishers,1990.[3]NurmiH.Approachestocollectivedecisionmakingwithfuzzypreferencerelations[J].FuzzySetsandSystems,1981,6(3):249-259.[4],.[J].,1997,17(9):22-66.[5],,.[J].,1997,17(3):8-15.[6],.[J].,1998.13(4):86-92.[7]KacprzykJ,FedrizziM.Asoftmeasurecofconsensusinthesettingofpartial(fuzzy)preferences[J].EuropeanJournalofOperationalResearch,1988,34(3):316-325.[8]BardossyA,DucksternL,BogardiI.Combinationoffuzzynumbersrepresentingexpertopinions[J].FuzzySetsandSystems,1993,57(2):173-181.[9]BUCKLEYJJ.Rankingalternativesusingfuzzynumbers[J].FuzzySetsandSystems,1985,15(1):21-31.[10]ChenSH.Rankingfuzzynumberswithmaximizingsetandminimizingset[J].FuzzySetsandSystems,1985,17(2):113-129.[11]KimK,ParkKS.Rankingfuzzynumberswithindexofoptimism[J].FuzzySetsandSystems,1990,35(2):143-150.[12]BortolanG,DeganiR.Areviewofsomemethodsforrankingfuzzysubsets[J].FuzzySetsandSystems,1985,15(1):1-19.[13]OscarP,JrDias.Rankingalternativesusingfuzzynumbers:Acomputationalapproach[J].FuzzySetsandSystems,1993,56(2):247-252.(80):[1],1[J].,1999,15(1):112117.[2]1[J]1,1990,(4):110114.[3]1[M].:,19971[4]1[M]1:,199016820017©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.