A note on fuzzy cardinals

In last years, a variety of papers on fuzzy sets and other fuzzy topics was concerned with set-algebraic operations for and properties of fuzzy sets. However, only few remarks are devoted to fuzzy cardinals. In classical set theory the cardinality of a set is a measure of its size or "power". In the fuzzy case one has to differentiate: there are measures of fuzziness and measures of power. Here measures of fuzziness are not our main concern. The interested reader may consult e.g. [1], [2], [5], [9]. Fuzzy cardinals as measures of power of fuzzy sets are considered e.g. in [2], [3], and [6]. To describe and compare these definitions needs some notation. A fuzzy set A over some universe of discourse X is a function A : X -> [0, 1]. Instead of A(x) for x e X we write also x e A for this membership value of x in A. The universe of discourse X shall be fixed throughout the paper. By ^(X) we denote the class of all fuzzy sets over X; for every A e ^(X), the support |A | of A is the classical set