TOPOLOGICAL CHARACTERIZATION FOR FUZZY REGULAR LANGUAGES

Abstract

We present a topological characterization for fuzzy regular languages:<br /> we show that there is a bijective correspondence between fuzzy regular languages<br /> and the set of all clopen fuzzy subsets with finite image in the induced fuzzy topological space of Stone space (Profinite space), and then we give a representation of closed fuzzy subsets in the induced fuzzy topological space via fuzzy regular languages. <br />Moreover, we prove that the induced fuzzy topological space has a basis consisting of leveled characteristic functions of the closure of cut languages of fuzzy regular languages.