Representational issues of preferences in the framework of a possibilistic ordinal decision model under uncertainty were introduced by Dubois and Prade a few years ago. In this framework, finite, linear, commensurate uncertainty and preference scales are assumed and decisions are ranked according to their expected utility in terms of Sugeno integrals. In this paper we generalise the model by allowing (i) to measure uncertainty and preferences on finite, distributive lattices with involution, and (ii) to formulate the utility expectations in terms of generalized Sugeno integrals where t-norms and t-conorms play a role. For these generalized utility functions we provide axiomatic characterisations. Finally, we also briefly comment the case of working with belief states that may be partially inconsistent, which is usual in case-based decision making problems or when several inconsistent sources of information are available.

This paper improves a previously proposed axiomatic setting for qualitative decision under uncertainty in the von Neumann and Morgenstern' style, where only ordinal linear scales are required for assessing uncertainty and utility. Two qualitative criteria are axiomatized in a finite setting: a pessimistic one and an optimistic one, respectively obeying an uncertainty aversion axiom and an uncertainty-attraction axiom. These criteria generalize the well-known maximin and maximax criteria, making them more realistic. They are suited to one-shot decisions and they are not based on the notion of mean value, but take the form of medians. Elements for a qualitative case-based decision methodology are also proposed, with pessimistic and optimistic evaluations formally similar to the expressions which cope with uncertainty, up to modifying factors which cope with the lack of normalization of similarity evaluations. Finally two extensions of the model are analysed: (i) the case of generalized possibilistic mixtures, using a t-norm instead of min, and (ii) the case of evaluating either preferences or uncertainty on Cartesian products of ordinal scales.