Abstract
Characterizations of an (is an element of, is an element of)-neutrosophic ideal are considered. Any ideal in a BCK/BCI-algebra will be realized as level neutrosophic ideals of some (is an element of, is an element of)-neutrosophic ideal. The relation between (is an element of, is an element of)-neutrosophic ideal and (is an element of, is an element of)-neutrosophic subalgebra in a BCK-algebra is discussed. Conditions for an (is an element of, is an element of)-neutrosophic subalgebra to be a (is an element of, is an element of)-neutrosophic ideal are provided. Using a collection of ideals in a BCK/BCI-algebra, an (is an element of, is an element of)-neutrosophic ideal is established. Equivalence relations on the family of all (is an element of, is an element of)-neutrosophic ideals are introduced, and related properties are investigated.