综合评价系统客观性指标权重的确定方法

200188:1000-6788(2001)08-0037-06庞彦军,刘开第,张博文(,056038):,.,,.,.:;;;:O212:ATheMethodofDeterminingtheObjectiveIndexWeightintheSyntheticEvaluationSystemPANGYan-jun,LIUKai-di,ZHANGBo-wen(InstituteofUncertainedMathematics,HebeiInstituteofArchitectureScience&Technology,Handan056038,China)Abstract:Inanysyntheticevaluationsystem,theweightofevaluationindexshouldbedetermined.Whentheexpertcan'tdeterminetheindexweightbyexperience,itisanimportantandconfusingproblemhowtoexploretheobjectivestandardfordeterminingtheindexweight.Thispaperdefinesthesimilarweightbysimilarfigures,andgivesamethodofdeterminingindexweightaccordingtoanobjectivestandard.Keywords:syntheticevaluationsystem;uncertainedmeasure;indexweight;similarweight1,,.,.,.:,,,,.,,,,..,,.,..,,,.,.1.1x1,x2,,xnn,X,X={x1,x2,,xn}.xiX,xixi,mI1,I2,,Im,I(:1999-12-09:(69675003);(696391,699319)),II={I1,I2,,Im}.xijixijIj,xim.xi=(xi1,xi2,,xim)xijp()c1,c2,,cp,U(),U={c1,c2,,cp}.ijk=(xijck)xijkck,:0(xijck)1(1)(xijU)=1(2)xijkl=1cl=kl=1(xijcl)(3)i=1,2,,n;j=1,2,,m;k=1,2,,p.(2)U,(3)U.,.(1)(2)(3),.(ijk)mp=i11i12i1pi21i22i2pim1im2imp,i=1,2,,n(4)xi,(4)jxij.1.2wjjIj,wj0wj1,mj=1wj=1(5)wjIj.1.3ik=(xick)ixikck,ik=mj=1wjijk,i=1,2,,n;k=1,2,,p(6)0ik1,pk=1ik=pk=1mj=1wjijk=mj=1pk=1ijkwj=mj=1wj=1(6)ik.(ik)np=11121p21222pn1n2np(7).(7)i(i1,i2,,ip)(8)xi.1.4(4)wj,(6)(7).Ij(j=1,2,,m),,,wj3820018?,,:wj=1m(j=1,2,,m).,(6)(7).(7)i(i1,i2,,ip)ixi,(4)m.,ikximck,ik=1m(i1k+i2k++imk)(9),(8)xi.,(ij1,ij2,,ijp)(10)(8)Ij,(10)(8),Ij,Ij.,.rj=1nni=1(ij1,ij2,,ijp)(i1,i2,,ip)T=1nni=1pk=1ijkik(11)wj=rjmj=1rj(12),0wj1,mj=1wj=1.rj,wj.wjIj.,,:1)n;,,,n!10.2)wj=1m(j=1,2,,m).3)(4)(6)(7).4)(4)(7)(11)rj,(12)wj.5)w=(w1,w2,,wm).w=(w1,w2,,wm)(4),(7),.,,.21:表1　湖泊水质评价标准Ijckc1c2c3c4c6I1:(gL-1)1423110660I2:(mgL-1)0.090.361.807.1027.10I3:(m)37122.40.550.17I4:(mgL-1)0.020.060.311.204.603982:表2　五个主要湖泊的实测数据xixijIjI1:(gL-1)I2:(mgL-1)I3:(m)I4:(mgL-1)x1:13010.300.352.76x2:10510.700.402.0x3:201.44.50.22x4:306.260.251.67x5:2010.130.50.23.,X={x1,x2,x3,x4,x5}I={I1,I2,I3,I4}={,,,}U={c1,c2,c3,c4,c5}={,,,,}2.11,1-4.123,.2,1234,.x13=0.35:()3()0.35,(3),0.3540200184,ABlAB:y=-10038x+5538,x=0.35,:135=0.526,x13=0.35(131,132,133,134,135)=(0,0,0,0.474,0.526):()x1(1jk)45=0000.9640.0360000.8390.1610000.4740.5260000.4510.549()x3(2jk)45=000.060.9400000.8190.1810000.610.390000.760.24()x3(3jk)45)=00.160.840000.280.720000.220.780000.360.6400()x4(4jk)45=000.920.080000.160.8400000.210.790000.8620.138()x5(5jk)45=00.160.84000000.8490.1510000.8680.13200.320.68002.2:,(w1,w2,w3,w4)=14,14,14,14(5):ik=144j=1ijk,i=1,2,,5;k=1,2,,5:c1c2c3c4c5=(ik)55=0000.700.30000.020.780.2000.250.7500000.270.500.2300.120.380.430.07x1x2x3x4x5418(11):(r1,r2,r3,r4)=(0.543,0.552,0.471,0.497)(13)(12):(w1,w2,w3,w4)=(0.263,0.268,0.228,0.241)(14)(14),ik=4j=1wjijk:c1c2c3c4c5=(ik)55=0000.6950.305000.0160.7890.19500.2540.74600000.2850.5020.21300.1190.3850.4250.071x1x2x3x4x5(15)2.3=0.60.7,(15),,.2.4{c1,c2,c3,c4,c5}U,c1c2c3c4c5,ckk,qxi=5k=1kik(16)qx1=4.3qx2=4.18,qx3=2.75,qx4=3.96,qx5=3.45qx1qx2qx4qx5qx3,:,,,,.,,.,,.,.:[1],.[J].,1996,14(5):44-49.[2].[J].,1988,9(2):59-63.[3],.[J].,1991,12(5):88-91.[4].Fuzzy-Grey[J].,1990,8(3):60-67.[5].[J].,1997,17(9):1-8.4220018