On Characterizations of General Type-2 Fuzzy Grammar and Its Languages by General Type-2 Fuzzy Finite Automata
Shambhu Sharan, Rakesh Kumar, Nitish Kumar
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Source: Crossref
Published: May 19, 2026
DOI: 10.1142/s1793005727500736
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The motivation of this work is to introduce and study the concept of general type-2 fuzzy grammars and their correspondence with general type-2 fuzzy automata. In particular, we establish the formal equivalence between general type-2 fuzzy weak regular grammars and general type-2 fuzzy regular grammars, showing that both generate the same class of general type-2 fuzzy languages. Furthermore, it is proved that every general type-2 fuzzy regular grammar admits an equivalent general type-2 fuzzy automaton, and conversely, every general type-2 fuzzy automaton can be represented by an equivalent general type-2 fuzzy regular grammar. We also investigate the closure properties of the class of general type-2 fuzzy languages recognized by general type-2 fuzzy automata and show that it is closed under union, intersection, concatenation, and Kleene closure, whereas it is not closed under complementation. Finally, through a suitable example, we demonstrate that a context-free general type-2 fuzzy grammar may generate context-sensitive general type-2 fuzzy languages. These results provide a formal algebraic and automata-theoretic foundation for the further development of general type-2 fuzzy language theory.
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