Abstract
Three main semantics for membership functions seem to exist in the literature: similarity, preference and uncertainty. Each semantics underlies a particular class of applications. Similarity notions are exploited in clustering analysis and fuzzy controllers. Uncertainty is captured by fuzzy sets in the framework of possibility theory. The membership function of a fuzzy set is also sometimes a kind of utility function that represents flexible constraints in decision problems. This paper advocates the claim that progress in operational semantics of membership functions presupposes that these distinct semantics be acknowledged and related to more basic measurement issues in terms of distance, cost and frequency, on which scientific traditions exist.
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