Solution of a system of neutrosophic linear algebraic equation by LU decomposition method

Neutrosophic numbers and matrices extend classical fuzzy set theory by incorporating three components to represent uncertainty: truth membership, indeterminacy membership, and falsity membership degrees. Real neutrosophic matrices consist of neutrosophic numbers as their entries, offering a structure to model uncertain and imprecise information across various applications. This paper investigates operations on real neutrosophic matrices, such as addition, multiplication, and scalar multiplication, and defines how these operations function within the neutrosophic framework. The paper also examines the use of LU decomposition as an efficient method for solving systems of real neutrosophic linear algebraic equations. LU decomposition is a numerical technique that breaks down a matrix into lower and upper triangular matrices, enabling the solution of linear systems through forward and backward substitution.