熵在决策分析中的应用综述

234Vol.23No.4ControlandDecision20084Apr.2008:2007201207;:2007204228.:(70372011,70671006,70701003).:(1972),,,,,;(1965),,,,,.:100120920(2008)04203612061,2,2(1.,100029;2.,100083):,:Bayes,.:;;;Bayes;:C934:ASurveyofapplicationsofentropyindecisionanalysisZHOURong2xi1,LIUShan2cun2,QIUWan2hua2(1.SchoolofEconomicsandManagement,BeijingUniversityofChemicalTechnology,Beijing100029,China;2.SchoolofEconomicsandManagement,BeihangUniversity,Beijing100083,China.Correspondent:ZHOURong2xi,E2mail:[e-mail])Abstract:Entropyisespeciallysuitabletonaturescience,socialscienceandtheirintercrossdisciplines.Therefore,applicationsandresultsofentropyareintroducedindecisionanalysis,suchasprobabilitydistribution,utilityfunctions,Bayesiandecision,multiobjectivedecision,groupdecisionandotherdecisionproblems.Andfurtherapplicationsandresearchdirectionsarediscussedindetail.Keywords:Entropy;Probabilitydistribution;Utilityfunctions;Bayesiandecision;Multiobjectivedecision1Shannon[1]1948;Jaynes[2]1957,.,.,,199720062443,.,,.2,,.,Bayes,.2.1,?Jaynes[2]1957(MEP),,P(ME):maxH(P)=-log(dP(x)/dx)dP(x),s.t.dP(x)=1,dP(x)0;k(x)dP(x)=k,k=1,2,.1978,Aida[3].Alexis[4].Thomas[5]ME,.KesavanMEP[6]23()[7].[8211].,Abbas[12].Michael[13],,GARCH.2.2,,().Barron[14].,Soofi[15].[16],,.Lehrer[17],,..Candeal[18].Abbas[19],vonNeumann2Morgenstern.,Abbas[20],,,,.Yang[21]2,2,,Allais.Darooneh[22],.2.3Bayes,,,.Bayes.BayesBayes[23,24].Bayes,,,,,Bayes[25].[26,27],Bayes,Bayes.[28],.,[29]Bayes,.Vetschera[30],.[31]3,.[32].[33],,Bayes.2.42:()..[14,15].[34](orness),(OWA).Filev[35]OWA,.Fuller[36],,OWA.Majlender[37]Rnyi.Liu[38].Kojadinovic[39]Choquet,,Choquet,,.,[40],AHP,.[41],62634:.[42243],,.[44],.[45].,[46].[47],,.[48],.,.[49]Minimax,Fritz2John(FJ)MinimaxFJ.[50],,,.[51],,.[52],,,.[53]KKT,,,.2.5,.1994,Levy[54],Bordley,,.[55].[56],.[57][56],,-,,.[58],,.[59],,,.2.6[60],,.,[61],,.[62].[63],.[64],.[65].3.,,.,:.2Bayes,.,,:(1).Laplace.:.(2),,,.[19221].,().(3)2Bayes.,Bayes,.36323(4),,ShannonRnyi,.,,.,.,,,.(5),.,.,.,,,.(References)[1]ShannonCE.Amathematicaltheoryofcommunication[J].BellSystemsTechnicalJ,1948,27(3):3792428.[2]JaynesET.Informationtheoryandstatisticalmechanics[J].ThePhysicalReview,1957,106(2):6202630.[3]AidaCG,LazoV,RathiePN.Ontheentropyofcontinuousprobabilitydistributions[J].IEEETransonInformationTheory,1978,24(1):1202122.[4]AlexisDeVos.Theentropyofamixtureofprobabilitydistributions[J].Entropy,2005,7(1):15237.[5]ThomasMU.Ageneralizedmaximumentropyprinciple[J].OperationsResearch,1979,27(6):118821196.[6]KullbackS,LeiblerRA.Oninformationandsufficiency[J].TheAnnalsofMathematicalStatistics,1951,22(1):79286.[7]KesavanHK,KapurJN.Thegeneralizedmaximumentropyprinciple[J].IEEETransonSystems,ManandCybernetics,1989,19(5):104221052.[8]AlhassidAN,LevineRD.Analgorithmforfindingthedistributionofmaximalentropy[J].JofComputationalPhysics,1979,30(2):2502259.[9]MeadLR,PapanicolaouN.Maximumentropyintheproblemofmoments[J].JofMathematicalPhysics,1984,25(8):240422417.[10]ZellnerA,HighfieldRA.Calculationofmaximumentropydistributionsandapproximationofmarginalposteriordistributions[J].JofEconometrics,1988,37(2):1952209.[11]OrmoneitD,WhiteH.Anefficientalgorithmtocomputemaximumentropydensities[J].EconometricReviews,1999,18(2):1272140.[12]AbbasAliE.Entropymethodsforjointdistributionsindecisionanalysis[J].IEEETransonEngineeringManagement,2006,53(1):1462159.[13]MichaelR,EricJ.Entropydensitieswithanapplicationtoautoregressiveconditionalskewnessandkurtosis[J].JofEconometrics,2002,106(1):1192142.[14]BarronH,SchmidtCP.Senstivityanalysisofadditivemultiattributevaluemodels[J].OperationsResearch,1988,36(1):1222127.[15]SoofiES.Generalizedentropy2basedweightsformultiattributevaluemodels[J].OperationsResearch,1990,38(2):3622363.[16],.[J].,1994,24(4):4612469.(JiangDan,QianYu2mei.Effectriskentropy[J].JofChinaUniversityofScienceandTechnology,1994,24(4):4612469.)[17]LehrerE,SmorodinskyR.Relativeentropyinsequentialdecisionproblems[J].JofMathematicalEconomics,2000,33(4):4252439.[18]CandealJC,DeMiguelJR,IndurAinE,etal.Utilityandentropy[J].EconomicTheory,2001,17(1):2332238.[19]AbbasAE.Entropymethodsforadaptiveutilityelicitation[J].IEEETransonSystems,ManandCyberneticsPartA,2004,34(2):1692178.[20]AbbasAE.Maximumentropyutility[J].OperationsResearch,2006,54(2):2772290.[21]YangJP,QiuWH.Ameasureofriskandadecision2makingmodelbasedonexpectedutilityandentropy[J].EuropeanJofOperationalResearch,2005,164(3):7922799.[22]DaroonehAH.Utilityfunctionfrommaximumentropyprinciple[J].Entropy,2006,8(1):18224.[23].[M].:,2003.(YueChao2yuan.Decisiontheoryandmethod[M].Beijing:SciencePress,2003.)[24].[M].:,2001.(QiuWan2hua.Managementdecisionandapplicationentropy[M].Beijing:ChinaMachinePress,2001.)[25],.Bayes[J].,1991,6(4):2512259.(GuChang2yao,QiuWan2hua.ComplexentropyanditsapplicationinBayesdecisionanalysis[J].ControlandDecision,1991,6(4):2512259.)[26],.2[J].4634:,1997,12(4):3532356.(QiuWan2hua,YangMin.Improvementofinformation2decisionanalysis[J].ControlandDecision,1997,12(4):3532356.)[27],.2Bayes[J].,2001,21(8):14218.(QiuWan2hua,GaoJian2wei.Theentr