Abstract
In this paper, we first define the notion of a complete general fuzzy automaton with threshold c and construct an H - group, as well as commuta- tive 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, thresh- oldness 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 hy- pergroup.
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