The necessary and sufficient conditions for a fuzzy relation being Τ-Euclidean

Authors:
Wen Sheng Du;Bao Qing Hu;Yan Zhao
Affiliations:
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China;School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China;Department of Mathematics, College of Information Science and Technology, Jinan University, Guangzhou 510632, PR China
Venue:
Information Sciences: an International Journal
Year:
2013

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Abstract

The connections between special types of fuzzy relations and properties of fuzzy rough approximation operators have been established in recent years, but @?-Euclidean fuzzy relation has not been considered yet. In the present paper, the necessary and sufficient conditions for a fuzzy relation being @?-Euclidean are investigated in three different fuzzy rough approximation spaces. Meanwhile, it is proved that in (I, @?)-fuzzy rough approximation space, where I is an R-implication, the properties the @?-Euclidean (I, @?)-fuzzy rough approximation operators possess are just the same as those in rough fuzzy approximation space.