UNIFORM AND SEMI-UNIFORM TOPOLOGY ON GENERAL FUZZY AUTOMATA

Abstract

In this paper, we de ne the concepts of compatibility between two<br />fuzzy subsets on Q, the set of states of a max- min general fuzzy automaton<br />and transitivity in a max-min general fuzzy automaton. We then construct a<br />uniform structure on Q, and de ne a topology on it. We also de ne the concept<br />of semi-uniform structures on a nonempty set X and construct a semi-uniform<br />structure on the set of states of a general fuzzy automaton. We then construct<br />a semi-uniform structure on , the set of all nite words on , the set of<br />input symbols of a general fuzzy automaton and, nally, using these semi-<br />uniform structures, we construct two topologies on Q and and discuss their<br />properties.