Bipolar possibility theory in preference modeling: Representation, fusion and optimal solutions

The bipolar view in preference modeling distinguishes between negative and positive preferences. Negative preferences correspond to what is rejected, considered unacceptable, while positive preferences correspond to what is desired. But what is tolerated (i.e., not rejected) is not necessarily desired. Both negative and positive preferences can be a matter of degree. Bipolar preferences can be represented in possibilistic logic by two separate sets of formulas: prioritized constraints, which describe what is more or less tolerated, and weighted positive preferences, expressing what is particularly desirable.The problem of merging multiple-agent preferences in this bipolar framework is then discussed. Negative and positive preferences are handled separately and are combined in distinct ways. Since negative and positive preferences are stated separately, they may be inconsistent, especially in this context of preference fusion. Consistency can be enforced by restricting what is desirable to what is tolerated.After merging, and once the bipolar consistency is restored, the set of preferred solutions can be logically characterized. Preferred solutions should have the highest possible degree of feasibility, and only constraints with low priority may have to be discarded in case of inconsistency inside negative preferences. Moreover, preferred solutions should satisfy important positive preferences when feasible (positive preferences may be also inconsistent). Two types of preferred solutions can be characterized, either in terms of a disjunctive combination of the weighted positive preferences, or in terms of a cardinality-based evaluation.