Vector General Fuzzy Automaton: A Refining Analyzing

Abstract

This study aims to investigate the refining relation between two vector general fuzzy automata (VGFA) and prove that refining relation is an equivalence relation. Moreover, Also, we prove that if there exists a refining equivalence between two VGFA, then they have the same language. After that, by considering the notion of refining equivalence, we present the quotient of VGFA. In particular, we show that any quotient of a given VGFA and the VGFA itself have the same language. Furthermore, using the quotient VGFA, we obtain a minimal VGFA with the same language.