Abstract:

The purpose of this paper is to introduce and study the notion of various important forms of general type-2 fuzzy grammars, namely, the general type-2 fuzzy grammar in normal form, general type-2 fuzzy linear grammar, general type-2 fuzzy left linear grammar, and general type-2 fuzzy right linear grammar. We establish that each of these forms is equivalent to a general type-2 fuzzy regular grammar (except for an empty string) in the sense that they induce the same class of general type-2 fuzzy languages. These results not only generalizes classical equivalence theorems from fuzzy grammar theory but also provide a theoretical basis for the analysis and future development of general type-2 fuzzy grammar theory.