Abstract
In this paper we introduce the notion of Fuzzy ω -Automata as an accepting device for Fuzzy ω -languages. We define Fuzzy ω -Finite State Automata which accept Fuzzy ω -regular languages with different acceptance criteria. We also define Distributed Fuzzy ω -Finite State Automata which are a group of fuzzy ω -finite state automata working in unison to accept a language with different modes of acceptance like the t -mode, *-mode, = k -mode, ⩽ k -mode and ⩾ k -mode. We prove that Distributed Fuzzy ω -Finite State Automata accept the same set of languages as Fuzzy ω -Finite State Automata. Analogously we define Fuzzy ω -Pushdown Automata and Distributed Fuzzy ω -Pushdown Automata along with the different acceptance criteria and modes of acceptance for the distributed case. The class of languages accepted by Fuzzy ω -Pushdown Automata is fuzzy CFL ω while the class of languages accepted by Distributed Fuzzy ω -Pushdown Automata contains CFL ω . We give proofs to show that all modes of acceptance are equal in the case of Distributed Fuzzy ω -Pushdown Automata. We also define L -Fuzzy ω -Automata and give some examples to show how it can be used to accept some non-fuzzy languages which are not accepted by their classical counterparts.
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