Group Fuzzy Languages and its Generalizations

Abstract

In fuzzy language theory, every monoid is the syntactic monoid of some fuzzy language. By using this result the properties of fuzzy language can be studied by the algebraic properties of the syntactic monoids. There are so many methods for studying fuzzy languages. We adopt the above method to analyze different class of fuzzy languages and also characterize certain varieties of fuzzy languages. In this paper we give the variety description of group fuzzy languages and also provide the Eilenberg variety theorem for the class of group fuzzy languages. Moreover we described a fuzzy language whose syntactic monoid is isomorphic to the group Zn.

Keywords

• syntactic congruence
• group fuzzy language
• pseudovariety