Fuzzy sets in categories of sets with similarity relations

Abstract

Several examples of categories K of sets with similarity relations are investigated. Objects of K are pairs (A, δ), where A is a set and d is a similarity relation on A with values in an MV-algebra Ω A fuzzy set t in (A, δ) in a category K (in symbol t ⊂∼K (A, δ)) is then defined as a morphism t: (A, δ) → (Ω,→) in a category K. Some properties of these fuzzy sets are investigated in some special categories K.