Scalar evaluations of fuzzy sets: overview and applications

Abstract The different representations of a fuzzy set, by a membership function or as weighted collections of crisp sets, induce various ways (which may sometimes turn to be equivalent) of extending confidence measures (probability, belief, possibility,...) to fuzzy events, or more generally any evaluation dealing with sets (cardinality, distance, extremum over a set, average, perimeter,...) to fuzzy sets.

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