A categorical approach to lattice-valued fuzzy automata

Some uniform categorical theoretical treatment of automata and lattice-valued fuzzy automata using quantale theory is studied in this paper. First, L-relational sheaves on a monoid M and Q-enriched categories are introduced for quantales L and Q, the equivalence of the corresponding categories are proved next. Then lattice-valued (fuzzy) automata are described by Q-enriched categories. In fact, lattice-valued (fuzzy) automata are characterized by the category of generalized lattice-valued automata using the notions of Q-bimodules. Finally, some of the algebraic properties of behaviors of generalized lattice-valued automata are studied by using the technique of gluing of Q-bimodules.