Axiomatic Foundations for Qualitative/Ordinal Decisions with Partial Preferences

Abstract

The representational issues of preferences in the framework of a possibilistic (qualitative/ordinal) decision model under uncertainty, were originally introduced few years ago by Dubois and Prade, and more recently linked to case-based decision problem by Dubois et al.. In this approach, the uncertainty is assumed to be of possibilistic nature. Uncertainty (or similarity) and preferences on consequences are both measured on commensurate ordinal scales. However, in case-based decision problems, similarity or preferences on consequences may sometimes take values that are incomparable. In order to cope with some of these situations, we propose an extension of the model where both preferences and uncertainty arc graded on distributive lattices, providing axiomatic settings for characterising a pessimistic and an optimistic qualitative utilities. Finally, we extend our proposal to also include belief states that may be partially inconsistent, supplying elements for a qualitative case-based decision methodology.