一种主客方协作式群体评价方法及其应用

18420108ChineseJournalofManagementScienceVol.18,No.4August,2010:1003-207(2010)04-0145-07一种主客方协作式群体评价方法及其应用张发明1,郭亚军2,易平涛2(1南昌大学经济管理学院,江西南昌330031;2东北大学工商管理学院,辽宁沈阳110004):,,;,,;,,,;,,:;;;:C934:A:2009-08-28;:2010-07-10:(70801013);(20080441094):(1980-),(),,,,:.1(),!,[1-8],,(),,,,(),!,!,[9-11],,,,,!:,,,,,,,!,,,,,!,,!,,,,,,[12],,,,:1),;2),,2,S={s1,s2,∀,sm},O={o1,o2,∀,on}psijsj(j=1,2,∀,m)oi(i=1,2,∀,n)(!),p0ijoi(i=1,2,∀,n)oj(j=1,2,∀,n,j#i)(),,p(s)p(o)(,n∃3,m∃3),M={1,2,∀,m},N={1,2,∀,n},P(s)=[p(s)ij]n%m=p(s)11p(s)12∀p(s)1mp(s)21p(s)22∀p(s)2m∀∀∀∀p(s)n1p(s)n2∀p(s)nm;P(o)=[p(o)ij]n%n=-p(o)12∀p(o)1np(o)21-∀p(o)2n∀∀∀∀p(o)n1p(o)n2∀-,(),,,:1,;2;3,,!,;4,!:,p(s),,y(s),y(s),,y(s),,p(o),,p(o),,,,,y(o),y(s)y(o),y*,,,,,,,,,113,,(),,,;,,,,,[12-16],[17-18],,(DM),DM,,,,,,,,,,M={1,2,∀,m},N={1,2,∀,n},Q={1,2,∀,q}&146&20101A=(a1,a2,∀,am),aj,aj=(a1,a2,∀,an)T(j=1,2,∀,m),A1,A2,∀,AqA(Ar(r=1,2,∀,q)),,∋Ai(Aj=,i#j,i,j=1,2,∀,q;)A1∗A2∗∀∗Aq=A,A1,A2,∀,AqAA1,A2,∀,AqA,q,AA1,A2∀,Aq2A1,A2∀,Aq(),Ar(r=1,2,∀,q)nr(1+nr+m-q+1),,nr=m,r1r2(r1,r2−Q),nr1∃nr2,A1,A2∀,AqAq3A=(a1,a2,∀,am),TDWA:Rn.R,TDWA(a1,a2,∀,am)=y=,qr=1r&y(Ar)(1)TDWA,TDWAy=(y1,y2,∀,yn)T;y(Ar)=yr=(y1r,y2r,∀,ynr)T,yir=,nrj=1w(r)ja(r)ij(i−N)A1,A2∀,ArAr,Ar={a(r)jr=1,2,∀,q;j=1,2,∀,nr},,qr=1nr=m,a(r)jArA(),=(1,2,∀,q),r−[0,1],r−Q,,r=1w=(w1,w2,∀,wm)A(),wj0(j−M),,mj=1wj=1,(r)=(w(r)1,w(r)2,∀,w(r)nr)Ar=(ar1,ar2∀,arnr),w(r)j=w(a(r)j)/,nrj=1w(a(r)j)w(a(r)j)()a(r)jw4A=(a1,a2,∀,am),TDWA:Rn.R,TDWGA(a1,a2,∀,am)=y=,qr=1y(Ar)r(2)TDWGA,TDWGAy,y(Ar)y=(y1,y2,∀,yn)T;y(Ar)=yr=(y1r,y2r,∀,ynr)T,3TDWATDWGA!!,(TDW)A=(a1,a2,∀,am)qA1,A2,∀,Aq,[19],(TDW)ps,(TDW),w1=w2=∀=wm=1/m=(1,2,∀,q)TP(s)1,P(s)2,∀,P(s)qp(s)q,P(s)r(r=1,2,∀,q)nr(1+nr+m-q+1),,nr=m,P(s)1,P(s)2,∀,P(s)qnr,P(s)'1,P(s)'2,∀,P(s)'q,P(s)'1,P(s)'2,∀,P(s)'qp(s)q,,,P(s)'1,P(s)'2,∀,P(s)'qP(s)1,P(s)2,∀,P(s)qP(s)2,∀,P(s)q,I!![14]:I=-,qr=1rlnr(3),,,!=,qr=1q-rq-1r(4),=(1,0,∀,0)T,!=1;=(0,0,∀,1)T,!=0;=(1/q,1/q,∀,1/q)T,!=05!!(1),!0,;!1,;!=05,,&147&4:1!!010305070902,04,06,08r:!!,,:max{-,qr=1rlnr}st!=,qr=1q-rq-1r,qr=1r=1,r−[0,1],r=1,2,∀,q(5)(5),r,,k(k+q)nr1,nr2,∀nrk,,*r1=*r2=∀=*rk=(r1+r2+∀+rk)/k(*r1,*r2,∀,*rk),rP(s)'1,P(s)'2,∀,P(s)'q,p(s)(TDW),oiy(s)i,y(s)=(y(s)1,y(s)2,∀,y(s)n)T4,,,,!oi(i=1,2,∀,n),oj(j#i),!,(p(o)ij),,,,y(s),,y,,,,,,,5y(s)i(i=1,2,∀,n),∀,yi(i=1,2,∀,n),,ysi=[ysLi,ysRi]=[max(0,yi-∀),yi+∀](6)∀(0∀5),,∀=2,;max(0,yi-∀)yi-∀0oi(i=1,2,∀,n)oj(j#i)p(o)ijyi(i=1,2,∀,n),,,,oi(i=1,2,∀,n),:oioj(j#i)oj(j#i)p(o)ijoi,p(o)ji:1):#ij=p(o)ij-ysRi,p(o)ijysRiysLi-p(o)ij,p(o)ijysLi(i,j=1,2,∀,n,i#j)2)∃ij,∃ij=#ij10;3)p(o)jip(o)/ji,p(o)/ji=p(o)ji(1-∃ij),,,6oi(i=1,2,∀,n),oi,,%i=1-!i/,ni=1!i(7)!i=,nj=1#ij,oi(i=1,2,∀,n)(7),,;&148&2010,p(o)'ji,oi(i=1,2,∀,n)y(o)i,y(o)i=%i&1n,nj=1p(o)'ji(8)%ioi(i=1,2,∀,n),p(o)'jioj(j=1,2,∀,n,j#i)oiy(o)=(y(o)1,y(o)2,∀,y(o)n)T,,,,,5y(s)y(o),,y*,y*i=&y(s)i+∋y(o)i(9)&∋,&+∋=1,,y(s)y(o),&=∋=1/2,y*:∃i=[min{y(s)i,y(o)i},max{y(s)i,y(o)i}],e(∃i)=max{y(s)i,y(o)i}-min{y(s)i,y(o)i},n(∃i)=(y(s)i,y(o)i)/2,y*n(∃i)e(∃i),y*i=(()i)=n(∃i)+)ie(∃i);i=1,2,∀,n(10))=()1,)2,∀,)n)T,y*y(s)y(o),,J()i)=,nk,h,k#h[u1(y(*)i-y(s)i)2+u2(y(*)i-y(o)i)2]stmin{y(s)i,y(o)i}+y(*)i+max{y(s)i,y(o)i},i=1,2,∀,n(11)u1,u2,u1+u2=1u1u2,;u1u2,(11))=()1,)2,∀,)n)T,(10),y*,y*=(y*1,y*1,∀,y*n)T6,105,105,(,,),P(s)P(o)(:,),(,)P(s)=45348676363837264886524793237563835337267426584528,P(o)=-53484-37252-47638-37426-:1)(095):S1={s1,s6,s10},S2={s2,s3,s8},S3={s4,s9},S4={s5},S5={s7}2)(5)(!!=080)=(039,039,018,002,002)T3)ysTDWA(1),ys=(483,589,434,490,532)T4)(6),o1=[283,683],o2=[389,789],o3=[234,634],o4=[290,690],o5=[332,732]5)yo,&149&4:(∀=2),(7)-(8),yo=(400,205,270,317,272)T6)(11),(u1=06,u2=04)y*=(450,435,368,421,428)T,o1o2o5o4o37:1),,,;2),!;3),,!,,;4),,;5),,,,,,,:1),,,;2),;3),:[1]ZelenyM..CriteriaDecisionMaking[M].Berlin:Springer!Verlag,1975.[2]HollowayC.A..Decisionmakingunderuncertainly:modelsandchoice[M].EnglewoodsCliff:Prenticehall,1979.[3]SaatyT.L..TheAnalytichierarchyprocess[M].NewYork:McGraw!Hill,1980.[4]HwangC.L.,YoonK..Multipleattributedecisionmaking[M].Berlin:Springer!Verlag,1981.[5]HwangC.L.,LinM.J..Groupdecisionmakingun!dermultiplecriteria:Methodsandapplications[M].Berlin:Springer!Verlag,1987.[6],.[J].,2009,31(7):41-44.[7].[M].:,1991.[8].[M].:,2002.[9].[M].:,2004.[10].[M].:,2007.[11]Yager.R.R..Inducedorderedweightedaveragingop!erators[J].IEEETransonSystems,Man,andCy!bernetics,1999,29(2):141-143.[12],,.[J].,2008(6):38-45.[13]XuZ.S.,DaQ.L..Anoverviewofoperatorsforagg!regatinginformation[J].InternationalJournalofIntel!ligentSystems,2003,18(9):953-969.[14]YagerR.R..Onorderedweightedaveragingaggreg!ationoperatorsinmulti!criteriadecisionmaking[J].IEEETransactionsonSystems,Man,andCyber!net!ics,1998,18(1):183-190.[15]YagerR.R..FamiliesofOWAoperators[J].FuzzySetandSystems,1993,59(1):125-148.[16]YagerR.R..ApplicationsandextensionsofOWAag!gregation[J].InternationalJournalMan!Machinestudy,1992,37(1):103-132.[17]XuZ.S.,DaQ.L..TheuncertainOWAoperator[J].InternationalJournalofIntelligentSystems,2002,17(6):569-575.[18],,.[J].,2007,22(5):515-519.[19],.[M].,2006.&150&2010AGroupEvaluationMethodandApplicationBasedonCollaborationofSu