Note on fuzzy languages

A fuzzy language is defined to be a fuzzy subset of the set of strings over a finite alphabet. The notions of union, intersection, concatenation, Kleene closure, and grammar for such languages are defined as extensions of the corresponding notions in the theory of formal languages. An explicit expression for the membership function of the language Z,(G) generated by a fuzzy grammar G is given, and it is shown that any context-sensitive fuzzy grammar is recursive. For fuzzy context-free grammars, procedures for constructing the Chomsky and Greibach normal forms are outlined and illustrated by examples.