Abstract

An axiomatic definition of fuzzy cardinalities for finite fuzzy sets, defined by means of a convex fuzzy set on the natural numbers, is presented in such a way that it includes the fuzzy cardinalities defined by authors like Zadeh, Ralescu, Dubois, Wygralak, and characterizes the cardinalities that fulfill the additivity property by means of the extended addition of fuzzy numbers. Such cardinalities result defined by two functions, one nondecreasing and the other nonincreasing in a similar way to the scalar cardinality (Fuzzy Sets and Systems 110 (2000) 175).

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