Ideals in BE-algebras Based on Lukasiewicz Fuzzy Set
DOI:
https://doi.org/10.29020/nybg.ejpam.v15i3.4467Keywords:
Fuzzy ideal, \L{}ukasiewicz fuzzy ideal, $\in$-set, $q$-set, $O$-setAbstract
For the purpose of applying the concept of Lukasiewicz fuzzy set to ideals in BE-algebras, Lukasiewicz fuzzy ideal is introduced, and its properties are studied. The relationship between fuzzy ideal and Lukasiewicz fuzzy ideal is discussed. Conditions for the Lukasiewicz fuzzy set to be a Lukasiewicz fuzzy ideal are provided, and characterizations of Lukasiewicz fuzzy ideal are displayed. Conditions in which three subsets, called ∈-set, q-set and O-set, are ideals are explored.
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