(untitled) (Contemporary Mathematics, 2025)
Matrices have significant contribution in the field of science and technology. It is often seen that fuzzy matrix theory theory cann’t address all types of uncertanity. In order to solve real life problems containing the neutrosophic phenomena, determinant and adjoint of a neutrosophic fuzzy matrix are required. The article introduces the notions of determinant and adjoint of neutrosophic fuzzy matrices. We shall define the idea of the neutrosophic matrix in which everyelement will appear with the degree of membership values of independent functions, namely membership, indeterminacy, and non-membership functions. Each degree of these membership values will be taken from the interval [0, 1]. With the help of this notion, we shall introduce the determinant and adjoint of a square neutrosophic fuzzy matrix. We shall investigate some basic properties, theorems and results of the determinant and adjointof a square neutrosophic fuzzy matrix. We shall justify these concepts by providing proof. Some properties and results shall be verified by providing suitable numerical examples. We shall give some definitions based on the newly defined concepts. The article reveals an innovative idea which contributes to find determiant and adjoint of neutrosophic fuzzy matrices generated from real-life problems. These newly introduced definitions will have applications in relevant science and technology research fields such as to solve linear equations containing neutrosophic fuzzy matrices.