Determinant-Theoretic Model for MCDM under Neutrosophic Hyper Soft Rough Matrices

In this paper, we explore the integration of determinant theory within the framework of Neutro sophic Hyper Soft Rough Matrix (NHSRM). We introduce a formal definition of the determinant for NHSRMs, establish its mathematical properties, and develop a determinant-based algorithm tailored for Multi-Criteria Decision-Making (MCDM). To highlight its practical utility, we conduct a comparative analysis with an existing score-based approach. To demonstrate the effectiveness of the proposed approach, an example is provided in which the determinant is computed and subsequently used to rank alternatives and assess the influence of different parameters. Additionally, a sensitivity analysis is performed to examine the robustness of the decision-making strategy under varying weight parameters. The results affirm that the determinant-based approach offers a more structured and reliable decision-making mechanism compared to score-based methods.