多属性群决策中决策者权重的确定方法

©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(2001)0420084206X,(,650093):,,,,:;;AHP;:F224:A,(),,,[1][2],,[3],,Kk.,(),KkKl,,DkDl,(),,,,,Bk.AHPDelphi,AHP,,1AHP,(AHP),[4]-[8]AHP,[9][10]AHP,AHP,s,D1,D2,,Ds,nAHPA(k)(k=1,2,,s)DkBkA(k)A(k)A(l)(lk)A(k)194(106)Vol.19,No.420017SystemsEngineeringJul.,2001X:2001205208:(0011106):(19662),,,,:,;(19562),,,,:,©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(1)k,A(k)A(l)(lk)B(2)k.B(1)kB(2)k,B(1)kB(2)kBk.1.1B(1)kA(k),A(k),A(k)A(k)B(1)k.B(1)k(1)CI(k)A(k)[11],A(k)CI(k)=K(k)max-nn-1,K(k)maxA(k),CI(k),A(k),A(k),CI(k)=0A(k),B(1)k:A(k)(k=1,2,,s),B(1)k=1s;A(k)(k=1,2,,s),CI(k)0,B(1)k=(CI(k))-Ask=1(CI(k))-A=(K(k)max-n)-Ask=1(K(k)max-n)-A(1),A1,A=1sk=1B(1)k=1sl(1ls),s-l,A(1),A(2),,A(l),A(l+1),A(l+2),,A(s),B(1)k=1l1+sk=l+1(CI(k))-A,(CI(k))-A1+sk=l+1(CI(k))-A,1kll+1ks,A1,A=1sk=1B(1)k=1(2)A(k)K(k)maxA(k)A(k)K(k)max=n,Dk=nöK(k)max,0Dk1,Dk,A(k),DkB(1)k,B(1)k=Dksk=1Dk=1öK(k)maxsk=11öK(k)max(2)(3)CHIA(k)[12]A=(aij)nn(ConsistencyHarmoniousWeightIndex):CHI=nj=1nbj(3),bj=ni=1aijai(j=1,2,,n),aj=ni=1aij(j=1,2,,n),ajAj[12]CHI1,A,CHI,A,A(k)CHI(k)B(1)k,B(1)k=CHIksk=1CHIk(4)(4)A(k)584,:©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(k)1A=(aij)nnW=(w1,w2,,wn)T,cij=bijöwi,i,j=1,2,,n,bij=aijni=1aij,C=(cij)nnA1[13]A1,C0=1111111112E=(eij)nnn,n2vec(E)=(e11,e21,,en1,e12,e22,,,en2,,e1n,e2n,,enn)TEA(k)C(k)=(c(k)ij)nn,vec(C(k))=(c(k)11,c(k)21,,c(k)n1,c(k)12,c(k)22,,,c(k)n2,,c(k)1n,c(k)2n,,c(k)nn)Tvec(C(k))vec(C0)=(1,1,,1n2)THk,cosHk=(vec(C(k)),vec(C0))öúvec(C(k))úõúvec(C0)ú(5)cosHk,vec(C(k))vec(C0),A(k)C0,A(k),cosHkB(1)k,B(1)k=cosHksk=1cosHk(6)B(1)k,A(k),,,n,K(k)max,nA(k),CHI(k)A(k),n,,,,(6)B(1)k1[14]54:A(1)=14681ö41531ö61ö5121ö81ö31ö21A(2)=14681ö41321ö61ö3131ö81ö21ö31A(3)=15691ö51131ö61121ö91ö31ö21A(4)=14581ö41231ö51ö2121ö81ö31ö21682001©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(5)=13581ö31121ö51131ö81ö21ö31:K(1)max=4.2071,K(2)max=4.2199,K(3)max=4.0340,K(4)max=4.0325,K(5)max=4.056854B(1)=(B(1)1,B(1)2,B(1)3,B(1)4,B(1)5)T1:(1)B(1)=(0.0554,0.0522,0.3374,0.3530,0.2020)T:(2)B(1)=(0.1953,0.1947,0.2037,0.2038,0.2025)T:(2):CHI(1)=0.9337,CHI(2)=0.9500,CHI(3)=0.9890,CHI(4)=0.9866,CHI(1)=0.9790,(4)B(1)=(0.1930,0.1963,0.2044,0.2039,0.2023)T:A(k)(k=1,2,,5)W(1)=(0.6132,0.2392,0.0855,0.0621)TW(2)=(0.6226,0.1964,0.1145,0.0665)TW(3)=(0.6684,0.1456,0.1249,0.0611)TW(4)=(0.6231,0.1939,0.1168,0.0662)TW(5)=(0.6056,0.1640,0.1612,0.0692)Tvec(C(1))=(1.0577,0.6781,1.2643,1.3060,1.1789,0.7554,0.4777,0.9694,0.7828,1.6722,0.9357,0.6441,0.9318,0.8959,1.6713,1.1498)Tvec(C(2))=(1.0418,0.8259,0.9441,1.2195,1.1013,0.8727,0.4987,1.2887,0.9325,1.4781,0.8454,0.4857,0.9178,0.7276,1.8716,1.0737)Tvec(C(3))=(1.0124,0.9293,0.9031,1.2308,1.0200,0.9368,1.0921,0.7430,1.0561,0.8077,0.9416,0.9624,0.8977,1.3736,1.0673,1.0917)Tvec(C(4))=(1.0189,0.8185,1.0873,1.1994,1.1005,0.8840,0.7337,0.8625,0.9440,1.2135,1.0068,0.8882,0.9170,1.1052,1.2235,1.0785)Tvec(C(5))=(0.9957,1.2256,0.7481,1.0869,0.9008,1.1085,1.1278,1.3136,1.1258,0.8317,0.8462,0.6561,0.9435,0.8713,1.3294,1.0318)T(5)cosH1=0.9497,cosH2=0.9485,cosH3=0.9892,cosH4=0.9900,cosH5=0.9829,(6):B(1)=(0.1954,0.1952,0.2035,0.2037,0.2022)T,B(1)kK(k)max-n,K(k)maxB(1)k,K(k)maxB(1)k,B(1)k,,K(k)maxB(1)k1.2B(2)ks,A(k),A(k),A(k)A(k)B(2)k1A(k)vec(A(k))=(a(k)11,a(k)21,,a(k)n1,a(k)12,a(k)22,,a(k)n2,,a(k)1n,a(k)2n,,a(k)nn)T,k=1,2,,s,784,:©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=(vec(A(i)),vec(A(j)))öúvec(A(i))úõúvec(A(j))ú,i,j=1,2,,s(7)vec(A(i))vec(A(j))0rij1,rij=1vec(A(i))=vec(A(j))rijvec(A(i))vec(A(j)),A(i)A(j)rk=sj=1,jkrkj,k=1,2,,s(8)rkA(k),rk,A(k),rkDkB(2)k,B(2)k=rksk=1rk,k=1,2,,s215,(7)R=(rij)55=10.98120.94180.97070.93540.981210.97390.98650.97970.94180.973910.99250.98330.97070.98650.992510.98300.93540.97970.98330.98301(8):r1=3.8291,r2=3.9213,r3=3.8915,r4=3.9327,r5=3.8814:B(2)1=0.1968,B(2)2=0.2015,B(2)3=0.2000,B(2)4=0.2021,B(2)5=0.1995113BkB(1)kB(2)k,DkBk=tB(1)k+(1-t)B(2)k,k=1,2,s,0t1,t=1ö22snW(k)=(W(k)1,W(k)2,,W(k)n)T,W(p)W(q)(p,q=1,2,,s)dpq=d(W(p),W(q))=12nj=1(W(p)j-W(q)j)2120d(W(p),W(q))1,d(W(p),W(q)),W(p)W(q)d=(dij)55=0d12d1sd210d2sds1ds20ddk=sl=1dkl(k=1,2,,s),dkW(k),dk,W(k),Bk=(1ödk)sk=1(1ödk),k=1,2,,sDk882001©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=LKk+(1-L)Bk,k=1,2,,s,0L1,L,,L=1,;L=0,4,AHP,,,,:[1].[J].,1995,13(4):43-46.[2],.[J].,1998,16(4):57-61.[3],.[J].,1996(3):52-56.[4],.[M].:,1995.[5],.[J].,1994,12(6):30-38.[6].[J].,1989(3):52-55.[7].AHP[J].,1997(6):76-80.[8],.AHP[J].,1995,4(1):66-68.[9].AHP[A].[C].:,1996.[10],,.AHP[J].,1999(3):24-29.[11].[J].,1993,2(3):69-72.[12],.[J].,1994,3(1):41-45.[13].[J].,1998,18(6):102-104.[14].AHP[J].,2000,14(3):106-110.TheMethodofDeterminingtheWeightoftheDecision-makerinMulti-attributeGroupDecision-makingSONGGuang2xing,ZOUPing(SchoolofManagementandEconomy,Kunm