Intuitionistic Fuzzy Finite Automata And Their Languages

Intuitionistic fuzzy finite automata theory is an important part of automata theory.The definition of intuitionistic fuzzy finite automata is based on intuitionistic fuzzy sets,which is a kind of new fuzzy set defined by Atanassov.It is shown that intuitionistic fuzzy finite automata is better than fuzzy finite automata in application, so the researches of intuitionistic fuzzy finite automata and their languages take important place.The equivalence of classical finite automata has been discussed.But deterministic fuzzy finite automata and nondeterministic fuzzy finite automata are not always equivalent for generalized t-norm "*".Recently,professor Li Yongming brings finite generated condition and weakly finite generated condition which are based on max - * composition inference,and discusses approximation properties of fuzzy automata in detail.Firstly,intuitionistic fuzzy recognizers and their languages and intuitionistic fuzzy finite automata and their languages which are based on "∨" and "∧" are studied under intuitionistic fuzzy sets in this paper,and the equivalence of deterministic intuitionistic fuzzy finite automata and intuitionistic fuzzy finite automata is proved.Secondly,we show that deterministic intuitionistic fuzzy finite automata and intuitionistic fuzzy finite automata based on generalized t-norms and s-norms are not equivalent,but they are equivalent if intuitionistic finite generated condition is satisfied;and intuitionistic fuzzy finite automata can be approximated by some deterministic intuitionistic fuzzy finite automata if weakly intuitionistic finite generated condition is satisfied.Moreover,the algebraic properties of languages recognized by intuitionistic fuzzy finite automata are discussed,i.e.the closure properties of the languages under the operations of union,intersection,complement,concatenation and Kleene closure and so on.Then intuitionistic fuzzy regular expressions and their languages are defined,and it is proved that the languages recognized by intuitionistic fuzzy regular expressions are equal to the languages recognized by intuitionistic fuzzy finite automata.Finally,the relationship between intuitionistic fuzzy regular languages with regular languages is discussed.