Categories of quantale-valued fuzzy automata: determinization and minimization

The objective of this paper is to introduce quantale-valued (in short Q-valued) fuzzy automata and its categories. The Q-valued fuzzy automaton in order to introduce here differs from the existing studies in the sense that the state-set itself is a quantale semimodule (in short Q-semimodule). Next, we introduce deterministic Q-valued fuzzy automaton and study the determinization of Q-valued fuzzy automata by using of Q-valued power set functor and show the existence of final object in the subcategory of category of deterministic Q-valued fuzzy automata. Finally, we show that the existence of minimal deterministic Q-valued fuzzy automata in the category of deterministic Q-valued fuzzy automata by using functorial maps.