\L{}ukasiewicz fuzzy ideals in BCK-algebras and BCI-algebras

Document Type : Research Paper


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


The notion of (closed) \L{}ukasiewicz fuzzy ideal is introduced, and several properties are investigated.
The relationship between \L{}ukasiewicz fuzzy subalgebra and \L{}ukasiewicz
fuzzy ideal is discussed, and characterization of a \L{}ukasiewicz fuzzy ideal is considered.
Conditions for a \L{}ukasiewicz fuzzy subalgebra to be a \L{}ukasiewicz fuzzy ideal are provided, and
conditions for the $\in$-set, $q$-set and $O$-set to be ideals are explored.