Topological Approaches in Characterization of Algebraic Structure of Fuzzy Multiset Finite Automata

This paper aims to provide the topological approaches in the characterization of the algebraic structure of fuzzy multiset finite automaton (FMFA). We have shown how the topological concepts of open sets and continuous functions can be utilized to characterize the algebraic structure of FMFA. The topological definition of a continuous function on fuzzy multiset finite automata and its structure preserving qualities are investigated. The operation preserving function between two fuzzy multiset finite automata is introduced, such functions are analogous to a homomorphism between algebraic structures but have an even stronger structure preserving nature than the continuous functions.