Recognizability of Intuitionistic Fuzzy Finite Automata-Homomorphic Images

Abstract

An intuitionistic fuzzy finite automaton with a unique membership transition on an input symbol is considered. It is shown that, if h : Γ * → Σ * is a morphism and h −1 (1) = 1, then the image of a recognizable subset of Γ * is a recognizable subset of Σ * and if h is fine, then the inverse image of recognizable subset of Σ * is recognizable. It is also proved that the shuffle product of any two recognizable sets is recognizable.Index Terms-Intuitionistic fuzzy sets, Intuitionistic fuzzy behavior, Intuitionistic fuzzy finite automaton, fine morphism, shuffle product.