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Other publications Cahiers de la Maison des Sciences Economiques Year : 2005

Decision making over necessities through the Choquet integral criterion

Abstract

Since von Neuman and Morgenstern's (1944) contribution to game theory, a rational decision maker will rank risky prospects according to the celebrated Expected utility criterion. This method takes lotteries i.e. (simple) probability distributions to represent risky prospects. If the decision maker follows the vN-M axioms (e.g.Kreps (1988)) then there exists a utility function such that any probability can be resumed to a lottery having for support the best and the worst state, where the probability that he wins the bet is given by its expected utility. Probalities are precise objects to model risk, but the way they do it is incoherent (Dubois and Prade (1988)). A familiar object in fuzzy set theory is the one of necessity or its dual version a possibility. In which case the occurence of an event is given by an interval which expresses the imprecision. Nevertheless the description of risk is coherent. Our concern is to rank different necessity measures and rank them according to the Choquet Expectation criterion (Choquet (1953)). If the decision maker follows our set of axioms then there exists a fuzzy set (Zadeh (1978)) such that any necessity can be resumed to a bet on being perfectly informed of the state which occurs or being totally ignorant, where the degree of information he will get is given by its Choquet expectation.
Depuis la contribution de von Neumann et Morgenstern (1944) à la théorie des jeux, un décideur classe des loteries selon le critère de l'espérance d'utilité. Les loteries sont des objets précis qui modélisent le risque, mais ceci d'une manière incohérente (Dubois-Prade (1988)). Un objet familier en théorie des ensembles flous est donné par les mesures de nécessité ou leurs duales, les mesures de possibilité. Ainsi l'occurrence d'un évènement est donnée par un intervalle qui exprime l'imprécision. Néanmoins la description du risque reste cohérente. Notre intérêt est de classer les mesures de nécessité et de les évaluer au travers du critère de l'espérance de Choquet (1953). Si un décideur suit nos axiomes alors il existe un ensemble flou (Zadeh (1978)) tel que toute nécessité se réduit à un pari entre être parfaitement informé ou être totalement ignorant de l'état qui va se réaliser et le degré d'information est donné par son espérance de Choquet.
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halshs-00197515, version 1 (14-12-2007)

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  • HAL Id : halshs-00197515 , version 1

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Yann Rébillé. Decision making over necessities through the Choquet integral criterion. 2005. ⟨halshs-00197515⟩
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Last update date on 5/18/24
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