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. However, some information is provided for such variables, in the form of possibility distributions over their domains. To tackle such problems, we eliminate the uncertain part of the problem, making sure that some desirable properties hold about the robustness of the problem’s solutions and its relationship with their preference. We also define semantics to order the solutions according to different attitudes with respect to the notions of preference and robustness.