Original Article

Neural Computing and Applications

, Volume 20, Issue 3, pp 319-328

First online:

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

  • Jianming ZhanAffiliated withDepartment of Mathematics, Hubei Institute for Nationalities Email author 
  • , Young Bae JunAffiliated withDepartment of Mathematics Education, Gyeongsang National University

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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.

Keywords

(p-Semisimple; quasi-associative; associative) BCI-algebra (∈, ∈ ∨ q)-fuzzy (p-; q- and a-) ideal (p-; q- and a-) ideal \((\overline{\in};\overline{\in} \vee \overline{q})\)-fuzzy (p-; q- and a-) ideal