综合加权评分法的综合权重确定新探

©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(2001)08200432061,2(1.,730070;2.,730070):,,,,L:;;;:O212.6aNewStudyonDeterminingtheWeightofIndexinSyntheticWeightedMarkMethodTAOJu2chun1,WUJian2min2(1.EconomicManagementCadreCollegeofGansu,Lanzhou730070,China;2.GansuAgriculturalUniversity,Lanzhou730070,China)Abstract:Accordingtotheproblemondeterminingtheweightsofindexesinthesyntheticweightedmarkmethod,thispaperanalysestheshortcomingofthemethodondeterminingtheindex’sweightsubjectivelyandobjectivelythatwehaveusedlargelynow.Meanwhile,givesthemethoddeterminingthesyntheticweightsofindexesthatincludebothsubjectivefavouritismandobjectiveinformation.Thusthesyntheticweightedmarkmethodbecomesmorereasonableandreliable.Keywords:multipleattributetest;syntheticweighted;markmethod;theweightofindex;subjectivefavouritism1,,,,,L,,,,L,L(),,,,L,,L,(),L:(),,L,(),L,L(),,,La:1999212221©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.={1,2,,n},m,J={1,2,,m},ijxij(i=1,2,,n;j=1,2,,m),X=(xij)nmZ,,,ZZ,,X:211:I1={};I2={};I3={};I1I2I3=I,IsIt=5(st,s,t,=1,2,3)2.1.1:yij=xijjI1-xijjI2ûxij-x3jûjI3(1)yij=xijjI1xjmax-xijjI2ûxij-x3jûjI3(2)x3jj(jI3),xjmax=max1in{xij}.2.2.2:yij=-xijjI1xijjI2-ûxij-x3jûjI3(3)yij=xjmax-xijjI1xijjI2-ûxij-x3jûjI3(4)212Zij=100(yij-yjminö(yjmax-yjmin),i=1,2,,n;j=1,2,,m(5)yjmin=min{yijûi=1,2,,n},yjmax=max{yijûi=1,2,,n}.Z=(zij)nm.3311,Z:A=(A1,A2,,Am)T(6)6mj=1Aj=1,Aj0(j=1,2,,m)3.2ZB=(B1,B2,,Bm)T(7)4420018©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=1Bj=1,Bj0(j=1,2,,m).3.3W=(w1,w2,,wm)T(8)6mj=1wj=1,wj0(j=1,2,,m).i:fi=6mj=1wjziji=1,2,,n(9)(),,,:minF(w)=6ni=16mj=1{L[wj-Aj)zij]2+(1-L)[(wj-Bj)zij]2}s.t.6mj=1wj=1wj0,j=1,2,,m(10)0L1,Z6ni=1z2ij0(j=1,2,,m),(10)Z:W=(LA1+(1-L)B1,LA2+(1-L)B2,,LAm+(1-L)Bm)T(11)Lagrange:L(W,K)=6ni=16mj=1{L[(wj-Aj)zij]2+(1-L)[(wj-Bj)zij]2}+2K6mj=1wj-1():5L5wj=6ni=1[2L(wj-Aj)z2ij+2(1-L)(wj-Bj)z2ij]+2K=05L5K=26mj=1wj-1=0,j=1,2,,m6ni=1wjz2ij+K=6ni=1[LAj+(1-L)Bj]z2ij,j=1,2,,m6mj=1wj=1m+1m+1,:Bmmem1eTm10wm1K=Cm11(12)Bmm=diag6ni=1z2i1,6ni=1z2i2,,6ni=1z2imem1=(1,1,,1)Twm1=(w1,w2,,wm)TCm1=6ni=1(LA1+(1-L)B1)z2i1,6ni=1(LA2+(1-L)B2)z2i2,,6ni=1(LAm+(1-L)Bm)z2imT():548©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=6ni=12z2ij52L5wj5K=252L5wi5wj=052L5K2=0Dk=6ni=1z2i10006ni=1z2i20006ni=1z2ik,k=1,2,,mDk0(k=1,2,,m),6ni=1z2ij0(j=1,2,,m),(10)Z(10):(12)BmmWm1+Kem1=Cm1eTm1Wm1=1(13)Bmm,B-1mm,(13)Wm1=B-1mmCm1+1-eTm1B-1mmCm1eTm1B-1mmem1em1(14)B-1mmCm1=[LA1+(1-L)B1,LA2+(1-L)B2,,LAm+(1-L)Bm]TeTm1B-1mmCm1=6mj=1[LAj+(1-L)Bj]=1Wm1=B-1mmCm1=[LA1+(1-L)B1,LA2+(1-L)B2,,LAm+(1-L)Bm]TZ4,Z4,,,1Z1A1(mm)B.C1(mm)123Áh=116.5Áh=117.0Á1Á2h=71180.730.911.371.01.50.56420018©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(A1)1(B1)1(C1)0.80.99.243.18.7212(B2)2(C2)0.0.8100.43.523.1313(B3)3(C3)4.40.95.640.750.442(A2)130.80.99.244.019.752213.80.96.243.546.462323.51.896.540.090.273(A3)121.60.98.440.719.983230.0.100.40.011.093313.40.796.444.064.7k127.416.139.9w1=0.34,w2=0.41,w3=0.14,w4=0.11k252.126.844.4BACk331.968.427.0B1A1C3R24.752.317.4A1B1C3,Z4112X=(xij):X=0.8099.243.10.0.8100.43.54.4095.640.70.8099.244.03.8096.243.53.51.896.540.01.6098.440.700100.40.03.40.796.444.04,,,3(:x34=42cm)Z,XZ(2):Y=(yij)=0.80.0.81.10.0.80.1.54.40.4.41.30.80.0.82.03.80.0.81.53.51.83.52.01.60.1.61.30.0.0.2.03.40.73.62.0(5)748©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=(zij)=18.20.018.20.0.44.00.44.4100.0.100.22.218.20.18.2100.86.40.86.444.479.5100.79.5100.36.40.36.422.20.0.0.100.77.338.981.8100.412,4,,:A1=0.5;A2=0.3;A3=0.1;A4=0.1A=(0.5,0.3,0.1,0.1)T,:hj=-(lnn)-16ni=1pijlnpij,Bj=(1-hj)6mk=1(1-hk)(j=1,2,,m):B=(0.18,0.52,0.18,0.12)T,pij=zij6ni=1zij,pij=0,pijlnpij=0(i=1,2,,n;j=1,2,,m)Z,(11),L=0.5w=(0.34,0.41,0.14,0.11)T.4.3(9)2Z4142,Áh=116.5(mm),0.73,0.5(mm)Z:[1]1[M]1:,19791[2],1[M]1:,19861[3]1[J]1,1993,(11):52-551(28)[5]HuberP.Stockmarketreturnsinthinmarkets2evidencefromtheoptionpricingmodels[J].AppliedFinancialEconomics,1997,7(5):68-73.[6]MaterYL.Nonlineardynamicsanddailystockreturnsonthetaiwanstockexchange[J].AppliedFinancialEconomics,1997,7(6):120-125.[7]PuttonewMT.Thelinearandnonlineardependenceofstockreturnsandtradingvolumeinthefinnishstockmarket[J].AppliedFinancialEconomics,1994,4(4):78-86.[8],,.[J].,1999,18(11):79-81.[9]RileyJ.Informationalequilibrium[J].Econometrica,1979,47(2):38-45.[10].[M].:,1997.8420018