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

S. Gomathi; A. Kavitha; R. Ramesh; E. Karuppusamy; L. Meenachi

Authors

S. Gomathi Department of Mathematics, Rathinam Technical Campus, Coimbatore, India;
A. Kavitha Department of Mathematics, Karpagam College of Engineering, Coimbatore, India;
R. Ramesh Department of Mathematics, Dr. Mahalingam College of Engineering and Technology, Pollachi, India;
E. Karuppusamy Department of Mathematics, Sri Krishna College of Engineering and Technology, Coimbatore, India;
L. Meenachi Department of Information Technology, Dr. Mahalingam College of Engineering and Technology, Pollachi, India;

Keywords:

Machine learning; Principal component analysis; Cubic spherical neutrosophic sets.

Abstract

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.