Uncertainty in Bipolar Preference Problems

Preferences and uncertainty are common in many real-life problems. In this paper, we focus on bipolar preferences and on uncertainty modelled via uncontrollable variables, and we assume that uncontrollable variables are specified by possibility distributions over their domains. To tackle such problems, we concentrate on uncertain bipolar problems with totally ordered preferences, and we eliminate the uncertain part of the problem, while making sure that some desirable properties hold about the robustness of the problem and its relationship with the preference of the optimal solutions. We also consider several semantics to order the solutions according to different attitudes with respect to the notions of preference and robustness.