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Decision-theoretic foundations of qualitative possibility theory

Didier Dubois, Henri Prade
IRIT - Université Paul Sabatier
31062 Toulouse Cedex (France)
e-mail: {dubois, prade}@irit.fr
Régis Sabbadin¹
INRA de Toulouse - Unité de Biométrie et Intelligence Artificielle
BP 27 - 31326 Castanet-Tolosan Cedex - FRANCE
e-mail : sabbadin@toulouse.inra.fr

Abstract:

This paper presents a justification of two qualitative counterparts of the expected utility criterion for decision under uncertainty, which only require bounded, linearly ordered, valuation sets for expressing uncertainty and preferences. This is carried out in the style of Savage, starting with a set of acts equipped with a complete preordering relation. Conditions on acts are given that imply a possibilistic representation of the decision-maker uncertainty. In this framework, pessimistic (i.e., uncertainty-averse) as well as optimistic attitudes can be explicitly captured.

The approach thus proposes an operationally testable description of possibility theory.