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

The notion of (closed) \L{}ukasiewicz fuzzy ideal is introduced, and several properties are investigated.The relationship between \L{}ukasiewicz fuzzy subalgebra and \L{}ukasiewiczfuzzy 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, andconditions for the \in-set, q-set and O-set to be ideals are explored.

Keywords:

\L{}ukasiewicz fuzzy set , (strong) \L{}ukasiewicz fuzzy subalgebra , (closed) \L{}ukasiewicz fuzzy ideal , q-set , O-set