Irreducible Fuzzy Multiset Finite Automaton

Abstract This study aims to investigate the algebraic properties of fuzzy multiset finite automaton (FMFA), giving a congruence relation. Using the equivalence classes, a minimal accessible complete FMFA is then presented. In addition, we define the concepts of admissible relation, admissible partition for FMFA and quotient FMFA. Further, we present an algorithm which determines an admissible partition for an FMFA and we suggest the time complexity of the algorithm. In particular, we introduce a connection between the admissible partition and the quotient FMFA and we show that any quotient of a given FMFA and the FMFA itself have the same language. Furthermore, using the quotient FMFA, we obtain an irreducible FMFA with the same language.