Elsevier

Fuzzy Sets and Systems

Volume 157, Issue 6, 16 March 2006, Pages 855-864
Fuzzy Sets and Systems

A categorical approach to lattice-valued fuzzy automata

https://doi.org/10.1016/j.fss.2005.08.002Get rights and content

Abstract

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.

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    This work is supported by National Science Foundation of China (Grant No. 60174016, 10226023), “TRAPOYT” of China and National 973 Foundation Research Program (Grant No. 2002CB312200).

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