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The purpose of the present work is to use the concepts of reachability and observability maps to provide a solution of a wellknown characterization of fuzzy regular languages. In between, we associate two deterministic fuzzy automata for a given deterministic fuzzy automaton and show that the reachability and observability maps of the given deterministic fuzzy automaton turn out to be morphisms in the category of deterministic fuzzy automata.

The purpose of this work is to use the concepts of reachability and coreachability maps to provide a solution of a well-known characterization for [Formula: see text]-valued multiset regular languages. In between, we associate two deterministic [Formula: see text]-valued multiset automata with a given deterministic [Formula: see text]-valued multiset automaton (DLMA) and show that the reachability and coreachability maps of the given DLMA turn out to be morphisms in the category of deterministic [Formula: see text]-valued multiset automata.

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