Some kinds of (is an element of(gamma), is an element of(gamma) boolean OR q(delta))-fuzzy ideals of BCI-algebras
The concepts of (is an element of(gamma), is an element of(gamma) boolean OR q(delta))-fuzzy (positive implicative, implicative and commutative) ideals and ((is an element of) over bar (gamma), (is an element of) over bar (gamma) boolean OR(q) over bar (delta))-fuzzy (positive implicative, implicative and commutative) ideals in BCl-algebras are introduced. Some new characterizations are investigated. In particular, we prove that a fuzzy set it of a BCl-algebra X is an (is an element of(gamma), is an element of(gamma) boolean OR q(delta))-fuzzy implicative ideal of X if and only if it is both an (is an element of(gamma), is an element of(gamma) boolean OR q(delta))-fuzzy positive implicative ideal and an (is an element of(gamma), is an element of(gamma) boolean OR q(delta))-fuzzy commutative ideal. Finally, we give some characterizations of three particular classes of BCI-algebras by these generalized fuzzy ideals. (C) 2010 Elsevier Ltd. All rights reserved.
(positive implicative, implicative and commutative) ideal (positive implicative, implicative and commutative) bcl-algebra (is an element of(gamma,) is an element of(gamma) boolean or q(delta))-fuzzy (positive implicative, implicative and commutative) ideal ((is an element of)over-bar(gamma,) (is an element of)over-bar(gamma) boolean or(q)over-bar(delta))-fuzzy (positive implicative, implicative and commutative) ideal