A Machine Learning Approach Using Principal Component Analysis and Cubic Spherical Neutrosophic Sets for MCDM

This study introduces two novel aggregation operators, namely the cubic spherical neutrosophic weighted arithmetic operator and the cubic spherical neutrosophic weighted geometric operator, to address multi-criteria decision-making problems under uncertainty. The proposed framework is built upon the concept of the cubic spherical neutrosophic set, where the evaluations of decision makers are transformed into a spherical representation by computing the center and radius of the sphere rather than simply averaging decision values. This transformation enables a more comprehensive modelling of truth, indeterminacy, and falsity degrees, while preserving the geometric structure of uncertainty. The cubic spherical neutrosophic weighted arithmetic operator and the cubic spherical neutrosophic weighted geometric operators satisfy essential mathematical properties such as idempotency, monotonicity, and boundedness, ensuring theoretical soundness. To determine the relative significance of decision criteria, principal component analysis is employed for dimensionality reduction and objective weight estimation based on variance contribution. A numerical case study on primary school selection in a particular region is provided, where the proposed operators combined with principal component analysis are used to rank the alternatives. Finally, a comparative analysis with existing MCDM approaches demonstrates strong correlation with benchmark results, while highlighting the enhanced discrimination power and robustness of the proposed methodology.