Interval-valued Fuzzy Sets, Possibility Theory and Imprecise Probability

Interval-valued fuzzy sets were proposed thirty years ago as a natural extension of fuzzy sets. Many variants of these mathematical objects exist, under various names. One popular variant proposed by Atanassov starts by the specification of membership and non-membership functions. This paper focuses on interpretations of such extensions of fuzzy sets, whereby the two membership functions that define them can be justified in the scope of some information representation paradigm. It particularly focuses on a recent proposal by Neumaier, who proposes to use intervalvalued fuzzy sets under the name “clouds”, as an efficient method to represent a family of probabilities. We show the connection between clouds, interval-valued fuzzy sets and possibility theory.