Categories of Automata and Languages Based on a Complete Residuated Lattice (original) (raw)

New Mathematics and Natural Computation, 2018

Abstract

The purpose of this paper is to introduce a new category of fuzzy automata based on complete residuated lattice. We introduce and study the categorical concepts such as product, equalizer and their duals in this category. Finally, we establish a construction of a minimal fuzzy automaton for a given fuzzy language in a categorical framework. The construction of such fuzzy automaton is based on derivative of a given fuzzy language.

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