基于相容性修正的群组决策排序算法

20041010:100026788(2004)10200862061,1,2(1.,400044;2.,200240):,,L,,,L:;;;:O223:AAlgorithmofSolvingWeightsforGroupDecisionMakingbyImprovingCompatibilityDONGYu2cheng1,CHENYi2hua1,WANGShuang2(1.CollegeofScience,ChongqingUniversity,Chongqing400044,China;2.CollegeofScience,ShanghaiJiaotongUniversity,Shanghai200240,China)Abstract:Anindexofthecompatibilityofthegroupdecisionmakingwasgiven.Bytheideaofminimizingthecompatibilityofthegroupdecisionmaking,amathematicalmodelofsolvingtheweightsofthegroupdecisionmakingwasgained.Andtheweproposedanalgorithmtomodifyapairofelementsoftheexpertjudgematrixes,bywhichthecompatibilityofthegroupdecisionmakingwaslessthanthatoftheoriginalone.Thentheconvergencetheoremforthisalgorithmwasestablishedanditspracticalitywasshowedbyexamples.Thepresentedmodelandalgorithmaremuchmoreprecisethatcommonmethods.ThesecanbeappliedtoGroupDSSwidely.Keywords:AHP(analytichierarchyprocess;groupdecisionmaking;compatibility;sort:2003210231:(1979-),,,,:,Email:[e-mail];(1957-),,,,:,1,()LAHP,,,L,,,()LL22,,(1,0),,(0,1),(),()(0.5,0.5),,LAHP,,,[1]L,,[2-6]LL,,L,,L©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.22.1,,,,,,,:??L[1]LL,L1AHPI,nE2,mE2,I(n,m)L2MR+n,I(n,m),AcMR+nc,w=(w1,w2,,wn)T,W=wiwj),(i=1,2,,n;j=1,2,,n)I(n,m)LI(n,m),AcW,acij=wiwjEcij.Ecij0,Ecij=1EcijZEcij=acijwjwi,acijL3I(n,m),61FijFnEcij+1Ecij-2c,CI(Ac,W)L3Ecij=1,i,j=1,2,,n,AcW,CI(Ac,W)=0LEcij1,CI(Ac,W),cL4I(n,m),6mc=161FijFnEcij+1Ecij-2,CI(I)L1I(n,m),CI(Ac,W)=0,(c=1,2,,m)CI(I)=0L,CI(I),LCI(I)CI(I),L2.2F(w)=6n-1i=16nj=i+16mc=1acijwjwi+acjiwiwj-2,AHP,,CI(I)=min(F(w))LLminF(w)=6n-1i=16nj=i+16mc=1acijwjwi+acjiwiwj-2,6ni=1wi=1.(1)(1)(2):minF(w)=m6n-1i=16nj=i+16mc=1acijwjmwi+6mc=1acjiwimwj-2,6ni=1wi=1.(2)(2),[7](2)w3,w36nj=16mc=1acijwjwi=6nj=16mc=1acjiwiwj,i=1,2,,n7810©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.w=(w1,w2,,wn)6ni=1wi=1,wi0,wRnLF(w)w3,,L,L1,L3,,,L,;,,,,,;,LLAc(c=1,2,,m)LErst=maxi,j,c(Ecij),Erst1,1FErstErst,Erts=1Erst,Ecij=Ecij,i,j,cs,t,rZAr=wiwjErijL1I(n,m),AcI(n,m)c,k,0A,CI(I)L1)k=0,Ac(k)=(ac(k)ij)=(acij);2)I(n,m)w(k)=(wk1,wk2,,wnk)TCI(I)(k);3)CI(I)(k)CI(I),6),;4)Ec(k)=(Ec(k)ij),Ec(k)ij=ac(k)ijw(k)jw(k)i,Erst=maxi,j,c(Ecij),Erst1,Er(k)=(Erij(k)),Erst(k)=Er(k)st-A,Erst(k)1,Erst(k)=1,Erts(k)=1Erst(k),Ecij(k)=Ec(k)ij,i,j,cs,t,r.Ar(k+1)=(ar(k+1)ij),ar(k+1)ij=w(k)iw(k)jErij(k).5)k=k+1,2);6)k,Ac(k),CI(I)(k),wk,k,Ac(k)c,CI(I)(k),wkZ2I(n,m),CI(I)(k)1,CI(I)(k+1)FCI(I)(k),limkCI(I)(K)=0.Q=w=(w1,w2,,wn)6ni=1wi=1,wRn,F(w(k+1))=minwQF(w)=minwQ6cm=16n-1i=16nj=i+1ac(k+1)ijwjwi+ac(k+1)jiwiwj-2F(wk+1)F6cm=16n-1i=16nj=i+1ac(k+1)ijw(k)jw(k)i+ac(k+1)jiw(k)iw(k)j-2=6cm=16n-1i=16nj=i+1Eij(k)+1Eij(k)-2.88200410©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.1,vs,t,r1FErst(k)Er(k)st,f(x)=x+1x,xE1,F(w(k+1))F6cm=16n-1i=16nj=i+1Ecij(k)+1Ecij(k)-26cm=16n-1i=16nj=i+1Ec(k)ij+1Ec(k)ij-2=F(w(k)).C.I(I)(k)=F(w(k)),CI(I)(k+1)CI(I)(k)ZPk,CI(I)(k)E0,CI(I)(k)ZlimkCI(I)(k)=inf{CI(I)(k)}.limkCI(I)(k)=inf{CI(I)(k)}=a0,1,Erst=maxi,j,c(Ecij),Erst1Z1,limkCI(I)(k+1)inf{CI(I)(k)}ZlimkCI(I)(k)=limkCI(I)(k+1)=inf{CI(I)(k)}Z41)ZI(n,m),MZAcW,acij=wiwjEcij,acij0,0,acij=0.F(w)=6cm=16n-1i=16nj=i+1acijwjwi+acjiwiwj-2+MZM,Z,acij0,Z2),ZI(n,m),Acc,wcAc(1),wI(n,m)Z[7],CIc6ni=16nj=i+1acijwjcwic+acjiwciwcj-2,AHPCIc=6ni=16nj=i+1acijwcjwci+acjiwciwcj-2Z3I(n,m),(CIc)(k)1(Ac)(k),limk(CIc)(k)=0Zwc(k)Ac(k),CIc(k)=6ni=16nj=i+1ac(k)ijwc(k)jwc(k)i+ac(k)jiwc(k)iwc(k)j-2Z:CIc(k)F6ni=16nj=i+1ac(k)ijw(k)jw(k)i+ac(k)jiw(k)iw(k)j-2F6mc=16ni=16nj=i+1ac(k)ijw(k)jw(k)i+ac(k)jiw(k)iw(k)j-2=CI(I)(k).0FCIc(k)FCI(I)(k),limkCIc(k)=0Z5A1,A2I(5,2)ZA1=122331ö211ö2211ö221221ö31ö21ö211ö21ö311ö221,A2=132431ö311ö2311ö221231ö41ö31ö211ö21ö311ö321.w=(0.38440.15290.24120.08660.1349),CI(I)=0.72Z9810©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.C.I(I)=0.2,(1)Z1Ak(A1)(k)(A2)(k)w(k)CI(I)(k)0.581.002.702.004.283.000.371.000.502.001.000.502.001.002.682.000.230.500.371.000.500.331.000.502.001.001.003.002.004.003.000.331.000.502.121.000.502.001.002.852.110.250.470.351.000.500.331.000.472.001.000.40160.13980.24250.07930.1368T0.18160.2151.002.352.004.103.000.431.000.602.001.000.501.671.002.372.000.240.500.421.000.500.331.000.502.001.001.003.002.004.003.000.331.000.601.961.000.501.681.002.351.960.250.510.431.000.500.331.000.512.001.000.40000.14790.22830.08400.1398T0.17610.05501.002.352.004.103.000.431.000.522.001.000.501.921.002.352.000.240.500.431.000.520.331.000.501.921.001.003.002.004.003.000.331.000.521.971.000.501.921.002.351.960.250.510.431.000.520.331.000.511.921.000.39920.14380.23400.08470.1384T0.1980,A,,Z,,A,,0.2FAF0.5,,Z6AHP,,L,L(CEC),,,[8,9],L(),,L,[2-6],L:[1].[J].,2000,20(2):92-96.WangLF,Compatibilityandgroupdecisionmaking[J].SystemsEnginerring-Theory&Practice,2002,20(2):92-96.[2],.[J].,2000,20(8):62-66.WeiCP,ZhangZM,Analgorithmtoimprovetheconsistencyofacomparisionmatrix[J].SystemsEngineering-Theory&Practice2000,20(8):62-66.[3],,.[J].,1995,15(9):36-43.WangZS,LiMQ,KouJS.FormationanalysisoftheinconsistencyofAHPmatrixandanadjustmentmethod[J].System