Publication:

Finite Nerode construction for fuzzy automata over the product algebra

The Nerode's automaton of a given fuzzy automaton A is a crisp-deterministic fuzzy automaton obtained by determinization of A using the well-known accessible fuzzy subset construction. This celebrated construction of a crisp-deterministic fuzzy automaton has served as a basis for various determinization procedures for fuzzy automata. However, the drawback of this construction is that it may not be feasible when the underlying structure for fuzzy automata is the product algebra because it is not locally finite. This paper provides an alternative way to construct a Nerode-like fuzzy automaton when the input fuzzy automaton is defined over the product algebra. This construction is always finite, since the fuzzy language recognized by this fuzzy automaton has a finite domain. However, this new construction does not accept the same fuzzy language as the initial fuzzy automaton. Nonetheless, it differs only in words accepted to some very small degree, which we treat as irrelevant. Therefore, our construction is an excellent finite approximation of Nerode's automaton.