Document Type : Research Paper


Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran


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.


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