A random set characterization of possibility measures

Several authors have pointed out the relationship between consonant random sets and possibility measures. However, this relationship has only been proven for the finite case, where the inverse Mobius of the upper probability induced by the random set simplifies the computations to a great extent. In this paper, we study the connection between both concepts for arbitrary referential spaces. We complete existing results about the lack of an implication in general with necessary and sufficient conditions for the most interesting cases.

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