Neural Computing and Applications

, Volume 20, Issue 3, pp 319–328

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

Original Article

DOI: 10.1007/s00521-010-0376-6

Cite this article as:
Zhan, J. & Jun, Y.B. Neural Comput & Applic (2011) 20: 319. doi:10.1007/s00521-010-0376-6


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.


(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

Copyright information

© Springer-Verlag London Limited 2010

Authors and Affiliations

  1. 1.Department of MathematicsHubei Institute for NationalitiesEnshiPeople’s Republic of China
  2. 2.Department of Mathematics EducationGyeongsang National UniversityChinjuKorea