运用离差最大化方法进行多指标决策与排序王应明

*王应明厦门大学自动化系,361005　　本文以工业经济效益的综合评价和排序为应用背景,提出了一种多指标决策与排序的新方法——离差最大化方法。该方法能够自动确定各评价指标间的加权系数,且概念清楚、涵义明确,排序结果准确、可信,不具有主观随意性。　多属性决策,经济效益分析,+多指标排序。UsingtheMethodofMaximizingDeviationstoMakeDecisionforMultiindiciesWangYingmingDepartmentofAutomation,XiamenUniversity,361005Abstract:Thispapertakesthesynthesizingevaluationofindustrialeconomicbenefitsbasedonsomeexamplesandproposesanewmethodnamedmaximizingdeviationsmethodformulti-indicesdecisions.Thenewmethodcanautomaticallydeterminetheweightcoefficientsamongthemultiindiceandalsocanobtaintheexactandreliableevaluationresultswithoutsubjectivi-ties.Keywords:Multiindicesdecisions,Multiindiciesranking,EconomicbenefitEvaluations,Maximizingdeviationsmethod.*　:19977301　　,,、、。,、,,。,,,。、、,。2　A={A1,A2,…,An},(、)G={G1,G2,…,Gm},AiGj()yij(i=1,2,…,n;j=1,2,…,m),Y=(yij)n×mAG“”,“”。,“”、“”、“”“”。,、、;,、;,,;·24·　　　1998　,。,G,G=∪4i=1KiKi∩Gj=O　i,j=1,2,3,4,i≠j(1)Ki(i=1,2,3,4)、、;O。,,,。,,。,Zij=yij-yminjymaxj-yminj,i=1,2,…,n,j∈K1(2)ymaxj、yminjGj。,Zij=ymaxj-yijymaxj-yminj,i=1,2,…,n,j∈K2(3)ymaxj、yminj(2)。,Zij=1-|yij-y*j|maxi|yij-y*j|,i=1,2,…,n,j∈K3(4)y*jGj。,Zij=1-q1j-yijmax{q1j-yminj,ymaxj-q2j},yijq1j1　yij∈[q1j,q2j],i=1,2,…,n,j∈K41-yij-q2jmax{q1j-yminj,ymaxj-q2j},yijq2j(5)[q1j、q2j]Gj,ymaxj、yminj(2)。Z=(Zij)n×m,,Zij。W=(W1,W2,…,Wm)T0,∑mj=1W2j=1(6)W,C=A1A2AnW1Z11W2Z12…WmZ1mW1Z21W2Z22…WmZ2m　　　　　　　W1Zn1W2Zn2…WmZnmG1G2　…　Gm(7)(SAW),AiDi(W)=∑mj=1ZijWj,i=1,2,…,n(8),Di(W),Di(W)Ai。,W,。W。,Gj(),Gj,0;,Gj,,。Gj,AiVij(W),Vij(W)=∑nk=1|WjZij-WjZkj|i=1,2,…,n,j=1,2,…,m　　(9)Vj(W)=∑ni=1Vij(W)=∑ni=1∑nk=1|Zij-Zkj|Wjj=1,2,…,m(10)Vj(W)Gj,。,W。,maxF(W)=∑mj=1Vj(W)=∑mj=1∑ni=1∑nk=1|Zij-Zkj|Wj(11),WmaxF(W)=∑mj=1∑ni=1∑nk=1|Zij-Zkj|Wjs.t.　∑mj=1W2j=1(12),·25·　7　　　W*j=∑ni=1∑nk=1|Zij-Zkj|∑mj=1∑ni=1∑nk=1|Zij-Zkj|2,j=1,2,…,m(13)W*=(W*1,W*2,…,W*m)TF(W)。,,W*,,W*,W~*j=W*j/∑mj=1W*j,j=1,2,…,m(14)W~*j=∑ni=1∑nk=1|Zij-Zkj|∑mj=1∑ni=1∑nk=1|Zij-Zkj|,j=1,2,…,m(15)　　,:(1)Z=(Zij)n×m;(2)W*,AiDi(W*)(i=1,2,…,n);(3),。3　《》199316、[1]。,,A={,,,,…,},16,G={G1,G2,…,G5},G1:(/);G2:(%);G3:();G4:();G5:(%),5,,,1。,W*=(0.5372,0.4399,0.3843,0.4701,0.3864)T,W~*=(0.2422,0.1983,0.1733,0.2119,0.1742)T,,、19921。1,、,,16、,;“”,,2;10、、、、、、,,,、、、,;、,、、,1615;,、、,,16、3。1992,,,,。,,,。(31)·26·　　　1998　,,。,,,。,,。1　A..,,19872　..,1997(6):1～63　..,1996(11):281(26)1　1992、0.24220.19830.17330.21190.1742(/)(%)()()(%)Di(W)4717716.618.8931.0515.770.78211433239.083.6529.808.440.328595902313.846.0626.5512.870.740224682110.593.5122.467.410.479464164613.244.6424.339.330.541242644610.162.3826.809.850.2888103838111.974.7926.4510.640.489055780810.294.5423.009.230.59943288697.682.1231.089.050.157314388128.923.3825.688.730.362873072110.874.1530.3611.440.351782484810.772.4230.7111.370.260111269259.343.0630.1110.840.257912232698.252.5832.578.620.111716282678.133.1729.259.170.222613215837.414.6635.3511.270.1454151　..,1993·31·　7