A bag theoretic fuzzy count and cardinality of fuzzy sets

The notion of Fuzzy sets introduced by Zadeh has been found to be a fruitful model in dealing with uncertainty in data. In order to define the cardinality of fuzzy sets the notion of sigma count was introduced by DeLuca and Termini. Cardinality of a fuzzy set as a fuzzy number, which is a simple but more natural extension of the approach of DeLuca and Termini was suggested by Zadeh. Our objective in this paper is to provide an alternate definition of fuzzy count using the notions of bag theory and establish its properties. Some of these properties were stated without proof by Zadeh and others are new properties for fuzzy counts.