Fuzzy sets in categories of sets with similarity relations

Several examples of categories K of sets with similarity relations are investigated. Objects of K are pairs (A, 6), where A is a set and 6 is a similarity relation on A with values in an MV-algebra ohm. A fuzzy set t in (A,delta) in a category K (in symbol t (subset of)(similar to)(K) (A, delta)) is then defined as a morphism t : (A, delta) ->(Omega, <->) in a category K.