Some kinds of View the -fuzzy filters of BL-algebras

Authors:
Xueling Ma;Jianming Zhan;Wiesław A. Dudek
Affiliations:
Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province, 445000, PR China;Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province, 445000, PR China;Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzee Wyspiańskiego 27, 50-370 Wrocław, Poland
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

The concepts of View the MathML source-fuzzy (implicative, positive implicative and fantastic) filters of BL-algebras are introduced and some related properties are investigated. Some characterizations of these generalized fuzzy filters are derived. In particular, we describe the relationships among ordinary fuzzy (implicative, positive implicative and fantastic) filters, View the MathML source-fuzzy (implicative, positive implicative and fantastic) filters and View the MathML source-fuzzy (implicative, positive implicative and fantastic) filters of BL-algebras. Finally, we prove that a fuzzy set F of a BL-algebra L is an View the MathML source-fuzzy implicative filter of L if and only if it is both an View the MathML source-fuzzy positive implicative filter and an View the MathML source-fuzzy fantastic filter.