On the Possibilistic-Based Decision Model: Characterization of Preference Relations Under Partial Inconsistency

Abstract

A qualitative counterpart to Von Neumann and Morgenstern's Expected Utility Theory of decision under uncertainty was recently proposed by Dubois and Prade. In this model, belief states are represented by normalised possibility distributions over an ordinal scale of plausibility, and the utility (or preference) of consequences of decisions are also measured in an ordinal scale. In this paper we extend the original Dubois and Prade's decision model to cope with partially inconsistent descriptions of belief states, represented by non-normalised possibility distributions. Subnormal possibility distributions frequently arise when adopting the possibilistic model for case-based decision problems. We consider two qualitative utility functions, formally similar to the original ones up to modifying factors coping with the inconsistency degree of belief states. We provide axiomatic characterizations of the preference orderings induced by these utility functions.