An Energy Framework For Spherical Fuzzy Rough Matrices and Its Use in Multi-Criteria Decision-Making

Abstract

This study proposes the basic idea underlying rough set serves as a technique for man aging information in relational databases. It is a distinctive field of uncertainity mathematics, strongly associated with fuzzy set theory. The integration of set theory in rough form along with spherical fuzzy set leads to the development of spherical fuzzy rough matrices, a powerful tool for managing uncertainity and vagueness in complex data environments. While spherical fuzzy sets enhance the descriptive power of conventional fuzzy models by representing the degrees of belonging, non-belonging and indeterminacy within a spherical framework, rough sets provide boundary-based approximations to handle indiscernibility in data. The combination of these two frameworks allows spherical fuzzy rough matrices (SFRM) to represent uncertain, imprecise and incomplete information in a more robust manner. This study demonstrates that the spherical fuzzy rough matrix acts as a crucial tool in strategic selection processes. The determinant and adjoint of the proposed matrix are formulated, and a ranking function based on its energy is derived. The study introduces an MCDM-based framework for the evaluation and ranking of different alternatives. To validate the effectiveness of the approach, numerical examples are presented, showing the practical applicability of the SFRM and its energy in addressing MCDM problems.