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 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.

Saeid and Jun introduced the notion of neutrosophic points, and studied neutrosophic subalgebras of several types in BCK=BCI-algebras by using the notion of neutrosophic points.

In the fuzzy set which is introduced by Zadeh, the membership degree is expressed by only one function so called the truth function. As a generalization of fuzzy set, intuitionistic fuzzy set is introduced by Atanassove by using membership function and nonmembership function.

This paper studies about the definition of MBJ – Neutrosophic set in 𝜷 – algebra, and introduce the concept of MBJ – Neutrosophic 𝜷 – subalgebra. Homomorphic image and inverse image of MBJ – Neutrosophic 𝜷 – subalgebra is provided. Also, Cartesian product of MBJ – Neutrosophic 𝜷 – subalgebra is studied.

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.