On Characterization of Algebraic Structure of Fuzzy Multiset Finite Automata

This paper enriches the theory of computing in the context of fuzzy sets and multisets. We have studied the computational model fuzzy multiset finite automaton (FMFA), which incorporates uncertainty about the next state of transition and multiple occurrences in the input set of automaton, and can be viewed as a generalized version of both classical automaton and fuzzy automaton. We have discussed the algebraic characterization of subautomaton of a FMFA, separatedness, strong connectedness and cyclic, directable and triangular FMFA in terms of equivalence classes induced by an equivalence relation defined on the state set of FMFA. Interestingly, for a given FMFA, a new FMFA is constructed which is a homomorphic image of the original FMFA. We have defined different poset structures associated with a given FMFA and showed that some of them are upper semilattices and discussed the inter-relationship of a given poset, a finite upper semilattice (FUSL), a FMFA and a poset/FUSL associated with a given FMFA. Finally, we have introduced the concept of decomposition of a FMFA in two different ways and characterized the strongly connected, triangular and directable FMFA.