由时序立体数据表支持的动态综合评价方法

:20000830:(98102005):(1952-),,,,2001年8月第22卷第4期东北大学学报(自然科学版)JournalofNortheasternUniversity(NaturalScience)Aug.2001Vol22,No.4:10053026(2001)04046404郭亚军1,潘建民2,曹仲秋3(1.,110004;2.,530012;3.,124010):,!,!,∀#!,!:;;:N94516:A()(),[1~4],,,,{xij(tk)},n()s1,s2,∃,sn,mx1,x2,∃,xm,t1,t2,∃,tT{xij(tk)},,([5]),()[6],[7],,!!!!,{xij(tk)},x1,x2,∃,xm,{xij(tk)}!{xij(tk)},tks1,s2,∃,sn()11.1[6]:tk(k=1,2,∃,T),,xjwj(tk)(j=1,2,∃,m;k=1,2,∃,T),yi(tk)=mj=1wj(tk)xij(tk)(1)k=1,2,∃,T;i=1,2,∃,nsitk!,hi=Tk=1exp{tk}yi(tk)(2)i=1,2,∃,n,,,=(2T)-1,hisi,[t1,tT]s1,s2,∃,sn,tk{xij(tk)}(j=1,2,∃,m;j=1,2,∃,n),![8],xj(j=1,2,∃,m)wj(tk),(j=1,2,∃,m;k=1,2,∃,T)1.2!,xij()=1TTk=1xij(tk)exp{tk}(3)j=1,2,∃,m;i=1,2,∃,n,,!,;=0,,=(2T)-1,{xij(tk)}{xij},2∀#!tk(k=1,2,∃,T),yi(tk)=mj=1wjxij(tk)(4)k=1,2,∃,T;i=1,2,∃,nwj(j=1,2,∃,m)s1,s2,∃,sn{xij(tk)},yi(tk)2=Tk=1ni=1(yi(tk)-!y)2,!y=1TTk=11nni=1mj=1wjxij(tk)=02=(yi(tk)-!y)2=(yi(tk))2=Tk=1[WHkW]=WTk=1HkW=WHW(5),W=(w1,w2,∃,wm),H=Hkm%m,Hk=XkXk(k=1,2,∃,T),Xk=x11(tk)∃x1m(tk)!!xn1(tk)∃xnm(tk),k=1,2,∃,T[8]31,:WW=1,WHmax(H)(),2max&W&=1WHW=max(H)Frobinius,H(hij0),H()W(W0),,WW,maxWHWs.t.&W&=1W03,11Table1Datesofmultidimensionaltimeseriest1x1x2x3x4t2x1x2x3x4t3x1x2x3x4t4x1x2x3x4s16010100.70166810800.70197011000.75197811200.7024s26810400.73177310900.75177511600.77177310900.7517s37010850.75187611250.78198011950.78227411150.7819s47511000.73207911600.80227911700.80217511600.8020s57011300.75237512000.82208112000.82208112000.8222,T=4,m=4,n=5{xij(tk)},Hk=(Xk)Xk(k=1,2,3,4):H1=500003.97203.50843.10273.9720500004.16334.68283.50844.1633500003.34113.10274.68283.341150000H2=500003.37214.30412.96353.3721500004.62903.28854.30414.6290500002.64072.96353.28852.640750000H3=500004.86594.39383.01414.8659500004.04812.35574.39384.0481500002.02043.01412.35572.020450000465第4期郭亚军等:由时序立体数据表支持的动态综合评价方法H4=500003.91470.97774.04503.9147500003.54362.36440.97773.543650000-1.28234.04502.3644-1.282350000Hk()(1)max=16.4309,(W1)=(0.2366,0.2723,0,2440,0,2471)(2)max=15.6823,(W2)=(0.2514,0.2627,0.2688,0.2171)(3)max=15.6126,(W3)=(0.2839,0.2700,0.2566,0.1894)(4)max=12.4713,(W4)=(0.3092,0.3065,0.1447,0.2396)H=4k=1(Xk)Xk=20000016.124713.184013.125316.124720000016.384012.691413.184016.38402000006.719913.125312.69146.7199200000()max=59.5715,W=(0.2651,0.2727,0.2401,0.2176),,yi(tk)22Table2Valuesofcomprehensiveevaluationt1t2t3t4y124.78224.60827.70827.78725.69525.99241.71039.648!!y235.55435.69932.26932.21933.65133.37128.83329.526!!y343.19243.31840.99140.96846.36546.67334.88935.742!!y445.74546.01150.40850.48544.80044.80441.19241.918!!y550.87850.48748.62548.53949.48949.16053.37653.167!!2yi(tk){si}(3)3,,!!{si}(yi(tk)),,3{si}Table3Rankingof{si}intimetk{si}!!t1s5∀s4∀s3∀s2∀s1s5∀s4∀s3∀s2∀s1t2s4∀s5∀s3∀s2∀s1s4∀s5∀s3∀s2∀s1t3s5∀s3∀s4∀s2∀s1s5∀s3∀s4∀s2∀s1t4s5∀s1∀s4∀s3∀s2s5∀s4∀s1∀s3∀s22,s1y1(tk);s2y2(tk);s3,s4,s5,?,4(1),(2)!,!,,(3)∀#!,[8]∀#!:[1]BorgulyaIA.Arankingmethodformultiplecriteriadecisionmarking[J].IntJournalofSystemsScience,1997,28(9):905-912.[2]SchenKS.AvoidingrankreversalinAHPdecisionsupportmodels[J].EuropeanJournalofOperationalResearch,1994,74:4607-4619.[3]PaulCN.Howdecisionmakersevaluatealternativesandtheinfluenceofcomplexity[J].ManagementScience,1998,44(8):1148-1168.[4]GeorgeWRG.Nonlineardecisionweightsinchoiceunderuncertainty[J].ManagementScience,1999,45(1):74-85.[5][J],1997,(7):94-98(WangYM.Decisionmakingmethodoftimeseriesmultiindicesidealpointanditsapplication[J].ChinaSoftScience,1997,(7):94-98.)[6][J](),1995,16(5):547-550(GuoYJ.Doublyweightingmethodfordynamiccomprehensiveevaluation[J].JournalofNortheasternUniversity(NaturalScience),1995,16(5):547-550.)[7],![J](),2000,21(2):140-143(JiangBT,GuoYJ.Evaluationmethodwith3dimension!466东北大学学报(自然科学版)第22卷attribute[J].JournalofNortheasternUniversity(NaturalScience),2000,21(2):140-143.)[8][M]:,1996.50-54(GuoYJ.Multiattributecomprehensiveevaluation[M].Shenyang:NortheasternUniversityPress,1996.50-54.)DynamicComprehensiveEvaluationMethodSupportedbyMultiDimensionalTimeSeriesGUOYajun1,PANJianmin2,CAOZhongqiu3(1.SchoolofBusinessAdministration,NortheasternUniversity,Shenyang110004,China;2.GuangxiTouristOffice,Nanning530012,China;3.LiaoheOilField,Panjin124010,China)Abstract:Manydynamiccomprehensiveevaluationproblemscanbemetfrequantlyintheprocessofeconomicalmanagementanddecisionmaking.Thehubofdynamiccomprehensiveevaluationistodeterminetheweightsforevaluationindexesatdifferenttime.Accordingtothefeatureofthecomprehensiveevaluationproblemsincaseofmultidimensionaltimeseries,byanewmethodnamedverticalandhorizontal!,scatterdegreeisproposedtodeterminetheweights.Andanexampleisgiven.Theproposedmethodissimpleprincipled,intuitive,andtheevaluationprocessofwhichiseasytounderstand.Keywords:multidimensionaltimeseries;scatterdegree;comprehensiveevaluation(ReceivedAugust30,2000)467第4期郭亚军等:由时序立体数据表支持的动态综合评价方法