On relationships among fuzzy approximation operators, fuzzy topology, and fuzzy automata

The fuzzy approximation operator associated with an approximation space (X, R) turns out to be a (saturated) Kuratowski fuzzy closure operator on X precisely when the relation R on X is reflexive and transitive. It is shown that all the level topologies of the fuzzy topology so obtained on X coincide. These observations are then applied to fuzzy automata. (C) 2002 Elsevier B.V. All rights reserved.