Congruences and homomorphisms of fuzzy automata

Concepts of congruences and homomorphisms of fuzzy automata are defined and Homomorphism theorem is proved. Lattices of congruences of fuzzy automata are described and an algorithm for computing the greatest congruence contained in an equivalence of a fuzzy automaton is presented. It is used for minimization procedures for both fuzzy automata with and without outputs. Connections with previously known minimization algorithms are discussed.