Title of article :
Commutative ideals of BCI-algebras based on Łukasiewicz fuzzy sets
Author/Authors :
Rezaei ، G.R. Department of Mathematics - University of Sistan and Baluchestan , Jun ، Y.B. Department of Mathematics Education - Gyeongsang National University
Abstract :
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.
Keywords :
Łukasiewicz fuzzy set , Łukasiewicz fuzzy subalgebra , Łukasiewicz fuzzy (commutative) ideal , 2 , set , q , set , O , set
Journal title :
Journal of Algebraic Hyperstructures and Logical Algebras
Journal title :
Journal of Algebraic Hyperstructures and Logical Algebras
