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

Abstract

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.

DOI: 10.5281/zenodo.15774099