Minimization of Deterministic Finite Automata with Vague (final) states and Intuitionistic\\ fuzzy (final) states

In this paper, relations among the membership values of generalized fuzzy languages such as intuitionistic fuzzy language, interval-valued fuzzy language and vague language are studied. It will aid in studying the properties of one language when the properties of another are known. Further, existence of a minimized finite automaton with vague (final) states for any vague regular language recognized by a finite automaton with vague (final) states is shown in this paper. Finally, an efficient algorithm is given for minimizing the finite automaton with vague (final) states. Similarly, it can be shown for intuitionistic fuzzy regular language. These may contribute to a better understanding of the role of finite automaton with vague (final) states or the finite automaton with intuitionistic fuzzy (final) states while studying lexical analysis, decision making etc.