TOPOLOGICAL CHARACTERIZATION FOR FUZZY REGULAR LANGUAGES

We present a topological characterization for fuzzy regular languages: we show that there is a bijective correspondence between fuzzy regular languages
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.
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.