A categorical approach to minimal realization for a fuzzy language.

Abstract In this study, we provide a general theory of minimal realization for a given fuzzy language in a category theory setting. We introduce categorical characterizations of a run map, reachability map, and observability map for a crisp deterministic fuzzy automaton. Finally, we show that all minimal realizations for a given fuzzy language are isomorphic to the Nerode realization for the same case. [ABSTRACT FROM AUTHOR]