Redefined fuzzy implicative filters

Authors:
Young Bae Jun;Yang Xu;Jun Ma
Affiliations:
Department of Mathematics Education (and RINS), Gyeongsang National University, Chinju 660-701, Republic of Korea;Department of Applied Mathematics, Southwest Jiaotong University Chengdu, 610031 Sichuan, China;Department of Applied Mathematics, Southwest Jiaotong University Chengdu, 610031 Sichuan, China
Venue:
Information Sciences: an International Journal
Year:
2007

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Abstract

Using the belongs to relation (@?) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (@q,@j)-fuzzy implicative filters where @q, @j are any two of {@?,q,@?@?q,@?@?q} with @q@?@?q is introduced, and related properties are discussed. Relations between (@?@?q,@?@?q)-fuzzy implicative filters and (@?,@?@?q)-fuzzy implicative filters are investigated, and conditions for an (@?,@?@?q)-fuzzy implicative filter to be an (@?,@?)-fuzzy implicative filter are provided. Characterizations of (@?,@?@?q)-fuzzy implicative filters are given, and conditions for a fuzzy set to be a (q,@?@?q)-fuzzy implicative filter are provided.