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

Authors:
Arun K. Srivastava;S. P. Tiwari
Affiliations:
Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi-221005, India;Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi-221005, India
Venue:
Fuzzy Sets and Systems
Year:
2003

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Abstract

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.