The theory of fuzzy set was introduced by Zadeh and he has shown meaningful applications of this notion in many fields of Engineering and Mathematical studies. Later Atanosov extended the fuzzy set into Intuitionistic fuzzy set by introducing a non-member. Recently the idea of cubic sets and related properties are investigated by Jun et al. All these fuzzy concepts were applied in various algebraic structures. Neggers and Kim presented the thought of β-algebras in which two operations are coupled in such a way that as to reflect the natural coupling which exists between the usual group operation. This study is to propose a new approach on a β-algebra using Cubic fuzzy set.

The conditions of β−algebra is enforced into the structure of cubic intuitionistic fuzzy settings. Furthermore, the concept of cubic intuitionistic β− subalgebra is expressed and its pertinent properties were explored. Also, discussed about the level set of cubic intuitionistic β−subalgebras and furnished some fascinating results on the cartesian product of cubic intuitionistic β−subalgebra. Moreover, the notion of -normed cubic intuitionistic β−subalgebras have been introduced and relevant results are studied.

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