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Preferences and uncertainty occur in many real-life problems. The theory of possibility is one non-probabilistic way of dealing with uncertainty, which allows for easy integration with fuzzy preferences. In this paper we consider an existing technique to perform such an integration and, while following the same basic idea, we propose various alternative semantics which allow us to observe both the preference level and the robustness w.r.t. uncertainty of the complete instantiations. We then extend this technique to other classes of soft constraints, proving that certain desirable properties still hold.