when upper probabilities are possibility measures

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1、FuzzySetsandSystems49(1992)65-7465North-HollandWhenupperprobabilitiesarepossibilitymeasuresDidierDuboisandHenriPradebetterunderstandthepowerofexpressivenessoflnstit~deRechercheenInformatiquedeToulouse(I.R.LT.)possibilityandnecessitymeasuresinordertoUniversitdPaulSabatier,Toulouse,Francerepres

2、entfamiliesofprobabilitymeasures.MakingthisconnectioncannotbuthighlighttheReceivedJune1991potentialroleofpossibilitytheoryintheproblemofapproximaterepresentationofAbstract:AcharacteristicpropertyisgivenforapairofprobabilisticevidencedescribedasinDeupperandlowerprobabilities(inducedbylowerprob

3、abilityboundsonafinitesetofevents)tocoincidewithpossibilityFinetti'sproblemintermsofknownconstraintsandnecessitymeasures.Approximationsofupperprobabil-ontheprobabilitiesofdistinguishedevents.itiesbypossibilitymeasuresarediscussed.TheproblemofThepaperfirstdevotestoapproximatecombiningpossibili

4、tydistributionsviewedasupperprobabil-solutionstoDeFinetti'sproblemdescribedbyitiesisinvestigated,andthebasicfuzzysetintersectionsarepossibilitymeasures,includingthecasewhenanjustifiedinthisframework.exactrepresentationisobtained.InthenextKeywords:Possibilitymeasure;necessitymeasure;probabil-p

5、art,weconsidertheproblemofcombiningity;upperprobability;fuzzyset.evidencedescribedbypossibilitydistributionsviewedasupperprobabilities.Aconditionisobtainedsuchthattwofamiliesofprobability1.Introductionmeasures,describedbymeansofpossibilitydistributions,wouldintersect.ItisinspiredbyInafamouspa

6、per,backinthethirties,DerecentfindingsofChateauneuf[4]ontheFinetti[5]hasconsideredtheproblemofequivalentproblemforbelieffunctions.Theaimdeterminingtheprobabilityofaneventgiventheistoevaluatethemeaningoffuzzysetprobabilitiesofafinitesetofotherevents.Thisintersectionoperatorsinthescopeoftheuppe

7、rproblemhasbeenstudiedbyAdamsandLevineandlowerprobabilityinterpretation.[1]andmorerecentlybyNilsson[16]intheframeworkofpropositionallogic;itcorrespondstoaproblemofreasoningunderuncertaintythatcanbesolvedbymeansoflinearprogramming2.Possibility