New construction method for the equivalence between two forms of deterministic fuzzy finite automata

Abstract Fuzzy automata and their languages provide a powerful tool for computational theory to study and deal with the fuzzy natural languages, and the equivalence among different forms of fuzzy automata provides a favorable basis for the flexible selection of computational models in practical applications. However, it has not been well solved that the proof of the equivalence between deterministic fuzzy finite automata with crisp initial state and fuzzy final state and deterministic fuzzy finite automata with fuzzy initial state and crisp final state. A direct construction method was given in Li and Pedrycz (2005). We later found the method has some deficiency, then an indirect proof method was given in Li et al.(2017). In this paper, we concern with two forms of deterministic fuzzy finite automata valued in lattice-ordered monoids, and a direct and effective construction method for the equivalence between them is given, then we also verify the new construction method with several examples.