fuzzy sets; equipollence of fuzzy sets; cardinal theory of fuzzy sets

The aim of this contribution is to propose an approach to comparing fuzzy sets from the cardinality point of view. The idea is based on a transformation of one fuzzy set to another one in some degree, where one-to-one mappings between suitable sets are used. To ensure the correctness of degrees in which there exist correspondences between fuzzy sets we introduce a class of sets and consider fuzzy sets and fuzzy classes with universes of discourse from this universe. We introduce a degree in which two fuzzy sets are equipollent and show that these degrees define a similarity relation on the class of all fuzzy sets. Some simplifications of the original definition of the concept of "being equipollent" are proposed and several properties are demonstrated.