HYPERGROUPS AND GENERAL FUZZY AUTOMATA

In this paper, we first define the notion of a complete general fuzzyautomaton with threshold c and construct an H_{nu}- group, as well as commutativehypergroups, on the set of states of a complete general fuzzy automatonwith threshold c. We then define invertible general fuzzy automata, discussthe notions of “homogeneity, “separation, “thresholdness connected, “thresholdnessinner irreducible and “principal and strongly connected, as appliedto them and use these concepts to construct a quasi-order hypergroup on aninvertible general fuzzy automaton. Finally, we derive relationships betweenthe properties of an invertible general fuzzy automaton and the induced hypergroup.

Keywords:

(General) Fuzzy automata , (Quasi-order) Hypergroup , Invertibility , Connectedness