HYPERGROUPS AND GENERAL FUZZY AUTOMATA

In this paper, we first define the notion of a complete general fuzzy automaton with threshold c and construct an $H_{nu}$?- group, as well as commutative hypergroups, on the set of states of a complete general fuzzy automaton with threshold c. We then define invertible general fuzzy automata, discuss the notions of “homogeneity, “separation, “thresholdness connected, “thresholdness inner irreducible and “principal and strongly connected, as applied to them and use these concepts to construct a quasi-order hypergroup on an invertible general fuzzy automaton. Finally, we derive relationships between the properties of an invertible general fuzzy automaton and the induced hypergroup.