Different models of automata with fuzzy states

In this paper we provide a general definition of automata with fuzzy stateswhich includes as its special cases automata used by Lin et al. [29], Liu and Qiu [30,31,42]and Xing et al. [56] in the study of fuzzy discrete event systems, as well as various typesof automata constructed in [14,15,18,32] for the purpose of the determinization of fuzzyautomata. We explain the relationships between these differentmodels of automata withfuzzy states and showthat every crisp-deterministic fuzzy automaton can be transformedinto a language-equivalent automaton with fuzzy states, and vice versa