一种群体评价一致性合成方法

200077:1000-6788(2000)07-0052-06赵海燕,曹　健,张友良(CIMS,210094):,,,.,.:;;:N94AnAggregatingMethodofGroupEvaluationBasedonConsensusDegreeZHAOHai-yan,CAOJian,ZHANGYou-liang(CIMSInstitute,NanjingUniversityofScience&Technology,Nanjing,210094)Abstract:Inthispaper,basedonusingtriangularfuzzynumbertorepresentevaluationopinion,anewmethodisproposedforaggregatingindividualfuzzyoptionsintoagroupfuzzyconsensusopinion.Afterfactorsaffectinggroupopinionhavebeenanalyzed,thecalculationmethodofweightofeachexpert'evaluationopinionisputout.Theaggregatingprocessandmethodarediscussedindetail.Thecharactersandpropertiesofthismethodarealsointroducedandproved.Anexamplegivenattheendofpapershowstheeffectivenessofthismethod.Keywords:groupevaluation;consensusdegree;weightofevaluation1,,,,.,,().,.,.,,.[1],,,,.,..[2],,..,.,:1998-12-04.,,,.,,.2,m,m,(l,m,r),l,r,,.,.(),{E,W,R,f},E={Eii=1,,n},W={Wii=1,,n},R={Rii=1,,n}.f,Ri(i=1,,n)R.2.11(a),R1=(1,2,3),R2=(5,6,7),,,,,,,1(b),.RiRj,Delphi[3],.a)b)12.2.,.2.2.1,,,,,,.iWi.2.2.2.2.1Ri=(li,mi,ri),Rj=(lj,mj,rj),S(Ri,Rj)=xmin(Ri(x),Rj(x))xmax(Ri(x),Rj(x))(1).,,2.,:2.2EiEjRi=(li,mi,ri),Rj=(lj,mj,5372rj),SijRiRj,Sij=S(Ri,Rj).,:2.3EiSi,:Si=1n-1nj=1,jiSij(2),,,:2.4,iSri:Sri=Sini=1Si(3)Ei,.,,.2.2.3,,,,.3,,W1=W4,W2W3.3,.E1E4.,E1E4,E1E4,E1E2,E4E3.,E1E3,,,E1E4..,.2.5SijEiEj,WjEj(j=1,2,,n).EiIi:Ii=1n-1nj=1,jiWjSij(4)2.6IiEi,EiIri.Iri=Iini=1Ii(5),,,5420007..2.2.4,.,..,:Ci=1Wi+2Sri+3Iri(6)1+2+3=1,13,23(6),,1=1,2=3=0.,2=1,1=3=0.,12,,21.Ci:2.1ni=1Ci=1ni=1Ci=ni=1(Wi+2Sri+3Iri)=ni=1Wi+2ni=1Sri+3ni=1Iri=1+2+3=12.3CiEiRi,Ci,Ri.,,:R=ni=1CiRi(7)3[4],.3.1:EiEj,Ri=Rj,R=Ri.,,.:R=ni=i=1Ci*Ri=Rini=1Ci=Ri(1Wi+2Si+3Ii)=Ri1ni=1Wi+2ni=1Si+3ni=1Iini=1Wi=1,ni=1Si=1,ni=1Ii=1R=Ri(1+2+3)=Ri3.2R,:ni=1RiR(0,1)ni=1Ri557ni=1Ri=ni=1Ri(ai,bi)=(maxni=1(ai),minni=1(bi))R=ni=1CiRi=ni=1Ciai,ni=1Cibiminni=1(ai)ni=1Cibimaxni=1(bi),minni=1(bi)ni=1Cibimaxni=1(bi)ni=1RiR3.3RiH(Ri),(8),H(Ri)=+-Ri(x)dx(8)minni=1(H(Ri))H(R)maxni=1(H(Ri))H(R)=Hni=1CiRi=ni=1H(CiRi)=ni=1(CiH(Ri))minni=1H(Ri))H(Ri)maxni=1H(Ri)minni=1H(Ri)ni=1CiH(R)maxni=1H(Ri)ni=1Ciminni=1H(Ri))H(R)maxni=1H(Ri)3.4,.,{(1),(2),,(n)}{1,2,,n},R=f(R1,R2,,Rn)=f(R(1),R(2),,R(n)).4E1,E2,E3,R1=(1,2,3),R2=(1.5,2.5,3.5),R3=(2,3,4),4(a).0.2,,.:1),2=1,1=3=0.(1):(Sij=10.3910.1420.39110.3910.1420.3911(2)(3),Sr:Sr=Sr1Sr2Sr3=0.2880.4240.288,(6),C,:C=S1S2S3=Sr=0.2880.4240.288,,E1E3,C1=C3,E1E3.(7)R(1)=3i=1CiRi=(1.5,2.5,3.5)2)56200071=0.6,2=0.3,3=0.1,W1=0.5,W2=0.3,W3=0.2(1)(7)SrIrCR(2):Sr=Sr1Sr2Sr3=0.2880.4240.288Ir=Ir1Ir2Ir3=0.2400.4500.310c=(123)W1W2W3Sr1Sr2Sr3Ir1Ir2Ir3=(0.4100.3500.240)R(2)=3i=1(ciRi)=(1.4152.4153.415)4(b).21,E1,,E1,.a)b)45.,,,,.,.,.,.:[1].[J].,1995,6(5):5963.[2]Hsi-MeiHsuetal.AggregationofFuzzyOptionsUnderGroupDecisionMaking[J].FuzzySetsandSystems1996,79(4):278285.[3]SaatyTL.TheAnalyticHierarchyProless[M].NewYork:McGray-Hill,1980.[4]AndrasBardossyetal.CombinationofFuzzyNumbersRepresentingExpertOptions[J].FuzzySetsandSystems,1993,57(1):173181.577