One-to-one correspondence between fuzzifying topologies and fuzzy preorders

Authors:
Jinming Fang;Piwei Chen
Affiliations:
Department of Mathematics, Ocean University of China, Qing Dao 266071, PR China;Department of Mathematics, Ocean University of China, Qing Dao 266071, PR China
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

This paper is devoted to the discussion of the relationship between fuzzifying topologies and fuzzy relations. A saturated fuzzifying topology can be generated by a reflexive fuzzy relation; and conversely, a fuzzy preorder can be generated by a fuzzifying topology. In fact, there exists a one-to-one correspondence between the set of all saturated fuzzifying topologies and that of all fuzzy preorders.