Scalar cardinalities of infinite fuzzy sets

This paper is devoted to the problem of the cardinality of infinite fuzzy sets, i.e. sets having an infinite support. The approach is an attempt to extend the classical cardinality of infinite crisp sets to the fuzzy case both with accumulation of the cardinalities of individual members of fuzzy sets and without it. The continuum hypothesis and fuzzy sets with different infinite supports are discussed for different definitions of infinite fuzzy sets´ cardinalities