Closure and Commutation of Fuzzy Regular Languages

The pumping lemma and Myhill-Nerode is very important in theory of formal languages and automata. In order to depict fuzzy regular language deeply. Firstly, the paper obtains the similar conclusion about fuzzy regular languages and then discusses the closed property under some operations. Finally the notion of commutative fuzzy regular language is introduced, some properties and equivalent depictions are obtained. This shows that it´s Boolean algebra. The results is a foundation for further researches on fuzzy finite state automata and fuzzy regular languages.