New types of fuzzy filters of BL-algebras

Authors:
Yunqiang Yin;Jianming Zhan
Affiliations:
Key Laboratory of Radioactive Geology and Exploration Technology Fundamental Science for National Defense, East China Institute of Technology, Fuzhou, Jiangxi 344000, China and School of Mathemati ...;Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province 445000, China
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

This paper introduces the concepts of (@a,@b)-fuzzy (implicative, positive implicative, fantastic) filters and (@b@?,@a@?)-fuzzy (implicative, positive implicative, fantastic) filters of BL-algebras, where @a,@b@?{@?"@c,q"@d,@?"@c@?q"@d,@?"@c@?q"@d}, @a@?,@b@?@?{@?"@c@?,q"@d@?,@?"@c@?@?q"@d@?,@?"@c@?@?q"@d@?}, @a@?"@c@?q"@d and @b@?@?"@c@?@?q"@d@?, and some related properties are investigated. Special attention is paid to (@?"@c@?,@?"@c@?@?q"@d@?)-fuzzy (implicative, positive implicative, fantastic) filters and (@?"@c@?,@?"@c@?@?q"@d@?)-fuzzy (implicative, positive implicative, fantastic) filters which are generalizations of (@?,@?@?q)-fuzzy (implicative, positive implicative, fantastic) filters and (@?@?,@?@?@?q@?)-fuzzy (implicative, positive implicative, fantastic) filters studied in Ma et al. (2008, 2009) [34,35]. It also points out that Examples 3.1.2, 3.1.9, 3.2.2, 3.2.9 and 3.3.9 in Ma et al. (2009) [35] are incorrect.