Journal
FUZZY SETS AND SYSTEMS
Volume 151, Issue 3, Pages 601-613Publisher
ELSEVIER
DOI: 10.1016/j.fss.2004.08.017
Keywords
rough set; fuzzy rough set; fuzzy relation; (TC) axiom; approximation operator; fuzzy topology
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This paper is devoted to the discussion of the relationship between fuzzy rough set models and fuzzy topologies on a finite universe. The (TC) axiom for fuzzy topology is proposed. It is proved that the set of all lower approximation sets based on a reflexive and transitive fuzzy relation consists of a fuzzy topology which satisfies (TC) axiom; and conversely, a fuzzy topology which obey (TC) axiom is just the set of all lower approximation sets under a reflexive and transitive fuzzy relation. That is to say, there exists a one-to-one correspondence between the set of all reflexive and transitive fuzzy relations and the set of all fuzzy topologies which satisfy (TC) axiom. (c) 2004 Elsevier B.V. All rights reserved.
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