FUZZY‐FUZZY AUTOMATA

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Abstract
Based on the concept of fuzzy sets of type 2 (or fuzzy‐fuzzy sets) defined by L. A. Zadeh, fuzzy‐fuzzy automata ate newly formulated and some properties of these automata are investigated. It is shown that fuzzy‐fuzzy languages characterized by fuzzy‐fuzzy automata are closed under the operations of union, intersection, concatenation, and Kleene closure in the sense of fuzzy sets of type 2, but are not closed under complement. The power of fuzzy‐fuzzy automata as an acceptor is the same as that of ordinary fuzzy automata and finite automata, though fuzzy‐fuzzy automata include fuzzy automata and finite automata as special cases. Finally, fuzzy‐fuzzy grammars are illustrated and it is shown that fuzzy‐fuzzy grammars with context‐free rules can generate context‐sensitive languages.

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