Some kinds of -fuzzy ideals of BCI-algebras

Authors:
Xueling Ma;Jianming Zhan;Young Bae Jun
Affiliations:
Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei Province, 445000, PR China;Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei Province, 445000, PR China;Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, South Korea
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

The concepts of (@?"@c,@?"@c@?q"@d)-fuzzy (positive implicative, implicative and commutative) ideals and (@?@?"@c,@?@?"@c@?q@?"@d)-fuzzy (positive implicative, implicative and commutative) ideals in BCI-algebras are introduced. Some new characterizations are investigated. In particular, we prove that a fuzzy set @m of a BCI-algebra X is an (@?"@c,@?"@c@?q"@d)-fuzzy implicative ideal of X if and only if it is both an (@?"@c,@?"@c@?q"@d)-fuzzy positive implicative ideal and an (@?"@c,@?"@c@?q"@d)-fuzzy commutative ideal. Finally, we give some characterizations of three particular classes of BCI-algebras by these generalized fuzzy ideals.