On the Cardinality and Power Set of Fuzzy Sets and Multiple Sets

A multiple set is a generalized version of a fuzzy set that deals with the uncertainty of an object along with its multiplicity. This work is a comparative analysis of the fundamental conclusions based on the cardinality of the classical set and fuzzy set. Several classical results based on fuzzy cardinality are then generalized to multiple set theory. An introduction to the concept of the power set of a multiple set is made, along with some basic results that support it. Furthermore, an extensive analysis of the power set properties of the fuzzy set is also carried out.