Uncertainty in Bipolar Preference Problems

Real-life problems can present several kinds of preferences, and may also contain some uncertain parts. In this paper we focus on problems with both positive and negative totally ordered preferences, and with some uncontrollable variables, which model the uncertainty of the problem. We call such problems uncertain bipolar problems (UBPs). After defining such problems, we propose to handle them by extending existing techniques to handle bipolar problems (BPs) and problems with uncertainty. In particular, we first eliminate the uncertainty of the problem, transforming a UBP into a BP. Then we solve the BP by associating to each solution both a degree of preference and a degree of robustness. Suitable semantics are then defined to order the solutions according to different attitudes with respect to these two notions.