Abstract
Regular fuzzy languages are characterized by some algebraic approaches. In particular, an extended version of Myhill-Nerode theorem for fuzzy languages is obtained.
Highlights
Fuzzy sets were introduced by Zadeh in 1 and since have appeared in many fields of sciences
In the texts Mordeson and Malik 3, Petkovic 6, Ignjatovic et al 7, and Shen 8, regular fuzzy languages have been characterized by the principal congruences principal right congruences, principal left congruences determined by fuzzy languages, which are known as Myhill-Nerode theorem for fuzzy languages
We have obtained an extended version of Myhill-Nerode theorem for fuzzy languages Theorem 3.9 which provides some algebraic characterizations of regular fuzzy languages
Summary
Fuzzy sets were introduced by Zadeh in 1 and since have appeared in many fields of sciences They have been studied within automata theory for the first time by Wee in 2. More on recent development of algebraic theory of fuzzy automata and formal fuzzy languages can be found in the book Mordeson and Malik 3 , the texts Malik et al 4, 5 , and Petkovic 6. In the texts Mordeson and Malik 3 , Petkovic 6 , Ignjatovic et al 7 , and Shen 8 , regular fuzzy languages have been characterized by the principal congruences principal right congruences, principal left congruences determined by fuzzy languages, which are known as Myhill-Nerode theorem for fuzzy languages. We characterize regular fuzzy languages by some kinds of generalized principal congruences resp., generalized principal right congruences, generalized principal left congruences. We obtain an extended version of MyhillNerode theorem for fuzzy languages
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