| Summary: | Rough set theory is a method of information processing for database systems. The neutrosophic matrix is a generalization of the fuzzy matrix, especially in handling indeterminacy situations. The concept of matrix theory and its energy in the neutrosophic environment help to determine the value of the uncertain matrix. In this paper, we correlate the rough set theory with the neutrosophic matrix theory to introduce the rough neutrosophic matrix (RNM). In this structure, lower and upper approximation neutrosophic matrices are used to deal with uncertain situations. We demonstrate that the given matrix plays a different role in decision-making situations and defined the proposed matrix's determinant, adjoint, algebraic properties and operations. Finally, derived the ranking function for a rough neutrosophic matrix's energy. The new multi-criteria decision-making (MCDM) approach was presented with the ranking formula, which was utilized to rank the alternatives, and numerical examples were provided to show how the proposed matrix and its energy could be applied to an MCDM problem.
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