权重信息完全未知且对方案有偏好的多属性决策法

20031212:100026788(2003)1220100204(,210007):.,,,,..:;;:C934:AAMethodforMultipleAttributeDecisionMakingwithoutWeightInformationbutwithPreferenceInformationonAlternativesXUZe2shui(InstituteofSciences,PLAUniversityofScienceandTechnology,NanjingJiangsu210007,China)Abstract:Thispaperstudiesthemulti2attributedecision2makingproblems,inwhichtheinformationaboutattributeweightsiscompletelyunknownandthedecision2maker(DM)haspreferenceinformationonalternatives.Aimingtothesituationswherethepreferenceinformationtakestheformofcomplementaryjudgementmatrix,wemakethedecisioninformationuniformbyusingalineartranslationfunctionbasedoncomplementaryjudgementmatrix,andestablishanoptimizationmodel.Wethengiveamethodforrankingthealternatives.Finally,anumericalexampleisgiventoillustratethedevelopedmethod.Keywords:multipleattributedecisionmaking;complementaryjudgementmatrix;model:2002210218:(Q02Y01):(1968-),,,,.1,[1-10].,[10],:1),;2),.,,,,.2,M={1,2,,m},N={1,2,,n}.,X={x1,x2,,xn},U={u1,u2,,um},w=(w1,w2,,wm)T,,wjE0,jM,6mj=1wj=1.xiX,jujU,xiujaij,©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.A=(aij)nm..,[11].,R=(rij)nm.xizi(w)=6mj=1rijwj,iN(1)wj(jM),.zi(w),xi;wj(jM),(1)..3[12]xi(iN),B=(bij)nn,,bij+bji=1,bii=0.5,bijE0,i,jN.,xi(iN)Bv=(blij)nn,blij=12[1+zi(w)-zj(w)]=121+6mk=1rikwk-6mk=1rjkwk=121+6mk=1(rik-rjk)wk,i,jN(2):blij+blji=1,blii=0.5,blijE0,i,jN.,B=(bij)nnBv=(blij)nn,fij=bij-blij=bij-121+6mk=1(rik-rjk)wk=126mk=1(rik-rjk)wk+(2bij-1),i,jN(3),w=(w1,w2,,wm)T,,(MOD)minF(w)=6ni=16nj=1f2ij=146ni=16nj=16mk=1(rik-rjk)wk+(2bij-1)2s.t.6mj=1wj=1,wjE0,jML(w,K)=F(w)+12K6mj=1wj-1(4)5L5wl=0(lM),126ni=16nj=16mk=1(rik-rjk)wk+(2bij-1)(ril-rjl)+12K=0,lM6mk=16ni=16nj=1(rik-rjk)(ril-rjl)wk=6ni=16nj=1(1-2bij)(ril-rjl)-K,lM(5)em=(1,1,,1)T,gqm=(g1,g2,,gm)T,D=(dlk)mm,,gl=6ni=16nj=1(1-2bij)(ril-rjl),l10112©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.M,dlk=6ni=16nj=1(rik-rjk)(ril-rjl),l,kM(6)(5)Dw=gqm-Kem(7)6mj=1wj=1,eTmw=1(8)(7)(8),w3=D-1(gqm-Kem)(9)K=eTmD-1gqm-1eTmD-1em(10)D(1).w3E0,(9)(1),,.,Pi,jN,6mk=1rikwk=6mk=1rjkwk,,.w30,[13](MOD),(1),,.1,D-1,D.vTDv=6ni=16nj=16mk=1(rik-rjk2)v2k+6ni=16nj=16ml=16mk=1,kl(rik-rjk)(ril-rjl)vkvl=6ni=16nj=16mk=1(rik-rjk)vk2=6ni=16nj=16mk=1rikvk-6mk=1rjkvk2=6ni=16nj=1[zi(v)-zj(v)]2(i,j),ij,zi(v)zj(v),((1):),v=(v1,v2,,vm)T0,vTDv0.D,D.,D,D-1.4,xi(i=1,2,,5),()[14]:(u1),(u2),(u3),(u4).1(:).1(u1)(u2)(u3)(u4)x15.205.204.730.473x210.086.705.711.599x35.254.203.820.473x49.725.255.541.313x56.603.753.300.803,;,uj201200312©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.wj(j=1,2,3,4)...:1)1A=(aij)54,rij=aijmaxi{aij},j=2,3;rij=mini{aij}aij,j=1,4A,R=(rij)54=10.7760.82810.516110.2960.9900.6270.66910.5350.7840.9700.3600.7880.5600.5780.5892)0.1-0.9xi(i=1,2,,5),B=(bij)54=0.50.60.50.90.70.40.50.40.70.50.50.60.50.70.20.10.30.30.50.10.30.50.80.90.5(9)w=(0.2014,0.1973,0.5893,0.0120)T3)w,(1)z1(w)=0.8544,z2(w)=0.8941,z3(w)=0.7293,z4(w)=0.8384,z5(w)=0.6169,x2:x1:x4:x3:x5.x2.:[1]ChenSJ,HwangCL.FuzzyMultipleAttributeDecisionMaking:MethodsandApplications[M].NewYork:Springer,1992.[2].[J].,1996,11(2):1-6.[3].[J].,2000,20(4):94-97.[4]KimJK,ChoiSH.Autilityrange2basedinformationgroupsupportsystemformulti2attributedecision2making[M].Computers&OperationsResearch,2001,28:485-505.[5],.[J].,2001,15(2):53-57.[6].[J].,2002,17(2):177-181.[7]XuZS,GuHF.Anapproachtouncertainmulti2attributedecision2makingwithpreferenceinformationonalternatives[A].Proceedingsofthe9thBellmanContinuumInternationalWorkshoponUncertainSystemsandSoftComputing[C],Beijing,China,2002,89-95.[8].[J].,2002,24(8):9-12.[9].[D].:,2002.[10]FanZP,MaJ,ZhangQ.Anapproachtomultipleattributedecisionmakingbasedonfuzzypreferenceinformationonalternatives[J].FuzzySetsandSystems,2002,131:101-106.[11],.[J].,1998,18(1):38-43.[12].AHP[J].,1999,19(7):97-101.[13]HartleyR.LinearandNonlinearProgramming:AnIntroductiontoLinearMethodsinMathematicalProgramming[M].EllisHorwoodLimited,England,1985.[14]1[J]1,1989,7(1):33-35.30112©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.