On algebraic study of fuzzy automata

This paper is towards the characterization of algebraic concepts such as subautomaton, retrievability and connectivity of a fuzzy automaton in terms of its layers, and to associate upper semilattices with fuzzy automata. Meanwhile, we provide a decomposition of a fuzzy automaton in terms of its layers and propose a construction of a fuzzy automaton corresponding to a given finite partially ordered set (poset). Finally, we establish an isomorphism between the poset of class of subautomata of a fuzzy automaton and an upper semilattice.