, Volume 20, Issue 3, pp 319-328

On \((\overline{\in},\overline{\in} \vee \overline{q})\) -fuzzy ideals of BCI-algebras

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Abstract

The concepts of \((\overline{\in},\overline{\in} \vee \overline{q})\) -fuzzy (p-, q- and a-) ideals of BCI-algebras are introduced and some related properties are investigated. In particular, we describe the relationships among ordinary fuzzy (p-, q- and a-) ideals, (∈, ∈ ∨ q)-fuzzy (p-, q- and a-) ideals and \((\overline{\in},\overline{\in} \vee \overline{q})\) -fuzzy (p-,q- and a-) ideals of BCI-algebras. Moreover, we prove that a fuzzy set μ of a BCI-algebra X is an \((\overline{\in},\overline{\in} \vee \overline{q})\) -fuzzy a-ideal of X if and only if it is both an \((\overline{\in},\overline{\in} \vee \overline{q})\) -fuzzy p-ideal and an \((\overline{\in},\overline{\in} \vee \overline{q})\) -fuzzy q-ideal. Finally, we give some characterizations of three particular cases of BCI-algebras by these generalized fuzzy ideals.