On effect algebras of fuzzy sets

Abstract

We introduce the category IE of effect algebras of fuzzy sets and sequentially continuous effect homomorphisms and describe its fundamental properties. We show that IE and the category ID of D-posets of fuzzy sets are isomorphic, hence the constructions and properties of ID related to applications to probability theory are valid for the corresponding effect algebras. We describe basic properties of categorical coproducts in ID and dually of categorical products in the corresponding category MID of measurable spaces. We end with remarks on fuzzy probability notions.