A natural interpretation of fuzzy set theory
A new and natural interpretation of fuzzy set theory is presented in a cumulative Heyting valued model for intuitionistic set theory that can consistently get various notions and properties of fuzzy sets, fuzzy relations and fuzzy mappings.
Abstract
We present a new and natural interpretation of fuzzy set theory in a cumulative Heyting valued model for intuitionistic set theory. By this interpretation we can consistently get various notions and properties of fuzzy sets, fuzzy relations and fuzzy mappings. We can consider notions such as operations of fuzzy subsets of different universes, fuzzy relations and mappings between fuzzy subsets. As far as fuzzy sets and fuzzy relations are considered as extensions of crisp sets and relations, this interpretation seems to be most natural.