Deterministic Fuzzy Automaton on Subclasses of Fuzzy Regular ω-Languages

In formal language theory, we are mainly interested in the natural language computational aspects of ω-languages. Therefore in this respect it is convenient to consider fuzzy ω-languages. In this paper, we introduce two subclasses of fuzzy regular ω-languages called fuzzy n-local ω-languages and Buchi fuzzy n-local !-languages, and give some closure properties for those subclasses. We define a deterministic fuzzy automaton acceptance conditions on fuzzy ω-languages and fuzzy n-local automaton. The relationship between deterministic fuzzy n-local automaton and two subclasses of fuzzy regular ω-languages are established and proved that every fuzzy ω-language accepted by a deterministic fuzzy automaton in 2-mode is a projection of a B¨uchi fuzzy 2-local !-language.