The concept of neutrosophic set (NS) developed by Smarandache is a more general platform which extends the concepts of the classic set and fuzzy set, intuitionistic fuzzy set and interval valued intuitionistic fuzzy set.

In this paper, we introduce a more general form of neutrosophic ideal, and investigate their properties.

The concepts of a BMBJ-neutrosophic subalgebra and a (closed) BMBJ-neutrosophic ideal are introduced, and several properties are investigated. Conditions for an MBJ-neutrosophic set to be a BMBJ-neutrosophic ideal in BCK/BCI-algebras are provided. Characterizations of BMBJ-neutrosophic ideal are discussed. Relations between a BMBJ-neutrosophic subalgebra, a BMBJ-neutrosophic subalgebra and a (closed) BMBJ-neutrosophic ideal are considered.

The notion of commutative MBJ-neutrosophic ideal is introduced, and several properties are investigated. Relations between MBJ-neutrosophic ideal and commutative MBJ-neutrosophic ideal are considered. Characterizations of commutative MBJ-neutrosophic ideal are discussed.

The concept of neutrosophic set (NS) developed by Smarandache is a more general platform which extends the concepts of the classic set and fuzzy set , intuitionistic fuzzy set and interval valued intuitionistic fuzzy set.

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