Neutrosophic Role-Differentiated α-Discounting Model with Residual Discrepancy Index for Multi-Criteria Curriculum Evaluation of Music Majors in Regional Universities

In regional universities, music students often face complex academic choices involving artistic, theoretical, and career-based subjects. These decisions are evaluated differently by students, teachers, and alumni, creating inconsistencies and uncertainty in curriculum planning. To address this, we propose a new neutrosophic multi-criteria decision-making model using a role-differentiated α-discounting approach. In this model, each evaluator group (student, teacher, graduate) is assigned its own set of weighted α values, depending on the consistency and reliability of their judgments. To quantify contradictions between these groups, we introduce a new mathematical index called the Neutrosophic Residual Discrepancy Index (NRDI). This index captures the remaining disagreement in neutrosophic evaluations across roles and influences the calculation of the α values dynamically. We also classify evaluation criteria into cognitive, creative, and operational categories, each handled by distinct discounting logic based on its nature and variability. The proposed model is applied to a case study involving core music curriculum components. Full computational steps are shown, including neutrosophic ratings, α-discounting transformations, and final decision ranking. The results demonstrate the model’s ability to balance subjective and objective evaluations, reduce contradiction, and support more informed curriculum design. This work offers a flexible, logic-based method for academic decision-making in creative disciplines where traditional models often fail.