Crossing cubic Lie algebras

An interval-valued fuzziness structure is an effective approach addressing ambiguity and for expressing people's hesitation in everyday situations. An N-structure is a novel technique for solving practical problems. This is beneficial for resolving a variety of issues, and a lot of progress is being made right now. In order to develop crossing cubic structures (CCSs), Jun et al. amalgamate interval-valued fuzziness and N-structures. In this manuscript, our main contribution is to originate the concepts of crossing cubic (CC) Lie algebra, CC Lie sub-algebra, ideal, and homomorphism. We investigate some properties of these concepts. In a Lie algebra, the construction of a quotient Lie algebra via the CC Lie ideal is provided. Furthermore, the CC isomorphism theorems are presented.