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.

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.

As a more general platform which extends the notions of the classical set, fuzzy set, interval valued fuzzy set, intuitionistic fuzzy set and interval valued intuitionistic fuzzy set, Smarandache developed the concept of neutrosophic set which consists of three member functions, so called truth membership function, indeterminacy membership function and falsity membership function.

The concept of neutrosophic set (NS) developed by Smarandache is a more generalplatformwhichextendstheconceptsoftheclassicsetandfuzzyset, intuitionistic fuzzy set and interval valued intuitionistic fuzzy set.

The notion of (i; j; k)-length neutrosophic subalgebras in BCK/BCI-algebras is introduced, and their properties are investigated. Characterizations of length neutrosophic subalgebras are discussed by using level sets of interval neutrosophic sets. Conditions for level sets of interval neutrosophic sets to be subalgebras are provided.

The notion of a neutrosophic quadruple BCK/BCI-number is considered, and a neutrosophic quadruple BCK/BCI-algebra, which consists of neutrosophic quadruple BCK/BCI-numbers, is constructed.

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.

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