TOPOLOGICAL CHARACTERIZATION FOR FUZZY REGULAR LANGUAGES

We present a topological characterization for fuzzy regular lan- guages: we show that there is a biject ive correspondence between fuzzy regu- lar languages and the set of all clopen fuzzy subsets with nite image in the induced fuzzy topological space of Stone space (Pronite 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.