THE CARDINALITY OF FUZZY-SETS AND THE CONTINUUM-HYPOTHESIS

Up to now, the research of the cardinality of fuzzy sets has hardly advanced since it is difficult to give it an appropriate definition. In this paper, we give a general definition of the cardinality of fuzzy sets based on the fuzzy mappings, and not only obtain a large part of the results with respect to the cardinality in Cantor's set theory, but also get many new properties of the cardinality of fuzzy sets. Especially, from the cardinality of fuzzy sets, we may gain some new ideas on the continuum hypothesis which is a well-known problem.