Commutative ideals of BCI-algebras based on Łukasiewicz fuzzy sets

Document Type : Original Article


1 University of Hatef, Zahedan, Iran

2 Department of Mathematics, University of Sistan and Baluchestan, Zahedan 98131, Iran

3 Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea


With the aim of applying the Łukasiewicz fuzzy set to commutative ideal in BCI-algebras, the concept of Łukasiewicz fuzzy commutative ideal is introduced, and its properties are investigated. The relationship between a Łukasiewicz fuzzy ideal and a Łukasiewicz fuzzy commutative ideal are discussed. After providing an example of a Łukasiewicz fuzzy ideal, not a Łukasiewicz fuzzy commutative ideal, conditions under which a Łukasiewicz fuzzy ideal can be a Łukasiewicz fuzzy commutative ideal are explored. Characterizations of Łukasiewicz fuzzy commutative ideals are displayed. Conditions under which $\in$-set, q-set, and O-set can be commutative ideals are found.