Fuzzy homomorphisms of algebras

In this paper we consider fuzzy relations compatible with algebraic operations, which are called fuzzy relational morphisms. In particular, we aim our attention to those fuzzy relational morphisms which are uniform fuzzy relations, called uniform fuzzy relational morphisms, and those which are partially uniform F-functions, called fuzzy homomorphisms. Both uniform fuzzy relations and partially uniform F-functions were introduced in a recent paper by us. Uniform fuzzy relational morphisms are especially interesting because they can be conceived as fuzzy congruences which relate elements of two possibly different algebras. We give various characterizations and constructions of uniform fuzzy relational morphisms and fuzzy homomorphisms, we establish certain relationships between them and fuzzy congruences, and we prove homomorphism and isomorphism theorems concerning them. We also point to some applications of uniform fuzzy relational morphisms.