Local Neutrosophic Rough Matrix, Its Energy, and Its Application

Objective: This study introduces the concept of the Local Neutrosophic Rough Matrix (LNRM) and energy of Local Neutrosophic Rough Set (LNRS), and explores its algebraic operations and properties. Method: The LNRM method is implemented to determine the truth, indeterminacy, and falsity of a matrix, and subsequently, the energy of LNRS is calculated to support the scaling of the order. Findings: The proposed approach is applied to validate the process of purchasing a quality machine for initiating a new project in a specific company. Finally, a figure provides a visual representation of the ranking of four machines. A comparative analysis is conducted to verify the effectiveness of the work. Novelty: This paper aims to address the limitations by introducing the energy concept within the framework of the local neutrosophic rough set. Furthermore, the proposed matrix-based computations are implemented using MATLAB software, which enables efficient handling of matrices of size 𝑛 × 𝑛. In contrast, existing studies performed computations solely through manual calculations without employing any software tools, thereby restricting matrix operations to small sizes, such as 3 × 3 or 4 × 4. Keywords: Rough Neutrosophic set; Local Rough set; Local Neutrosophic Rough set; Rough Neutrosophic Matrix; Local Neutrosophic Rough Matrix