Interval type-2 fuzzy automata and Interval type-2 fuzzy grammar

The purpose of the present work is to introduce and study the concept of interval type-2 (IT2) fuzzy grammar which recognizes the given IT2 fuzzy languages. The relationship between IT2 fuzzy automata and IT2 fuzzy (weak) regular grammars is discussed. Specifically, the results we obtained here are (i) IT2 fuzzy weak regular grammar and IT2 fuzzy regular grammar generate the same classes of IT2 fuzzy languages (ii) for a given IT2 fuzzy regular grammars, there exists an IT2 fuzzy automata such that they accept the same IT2 fuzzy languages, and vice versa. In addition, we define some operations on IT2 fuzzy languages and it is shown that IT2 fuzzy languages recognized by IT2 fuzzy automata are closed under the operations of union, intersection, concatenation and Kleene closure, but are not closed under complement.

Automated summary

This paper introduces and studies the concept of interval type-2 (IT2) fuzzy grammar for recognizing given IT2 fuzzy languages, discussing its relationship with IT2 fuzzy automata and IT2 fuzzy (weak) regular grammars. The results show that IT2 fuzzy weak regular grammar and IT2 fuzzy regular grammar generate the same classes of IT2 fuzzy languages, and there exists a correspondence between IT2 fuzzy regular grammars and IT2 fuzzy automata. Additionally, operations on IT2 fuzzy languages are defined and shown to be closed under union, intersection, concatenation, and Kleene closure, but not under complement.