Advances in Qualitative Decision Theory: Refined Rankings

Didier DuboisLluis GodoHenri PradeAdriana Zapico

A qualitative counterpart of Von Neumann and Morgenstern's Expected Utility Theory was proposed by Dubois and Prade in the mid nineties. In this decision theory uncertainty is assumed to be of a possibilistic nature and decisions can be ranked, via their associated possibility distributions on consequences, according to two qualitative criteria, one pessimistic and one optimistic. However, it may the case that the ranking induced by one of these criteria does not result in a total ordering of the decisions and it can be very interesting to refine the ranking by means of considering another criterion. In this paper we consider some natural refinements and provide the axiomatic characterization of the preference orderings induced by them.

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