Interval Valued Spherical Fuzzy Matrix in Decision Making

Recent advancements have demonstrated the potential to augment matrix theory with fuzzy, intuitionistic fuzzy, picture fuzzy, interval-valued picture fuzzy matrix concepts for enhanced decision-making applications. We introduce the interval valued spherical fuzzy matrix, extending the spherical fuzzy matrix, to effectively represent and manipulate uncertain and vague information with enhanced flexibility. This paper establishes definitions and theorems for Interval-Valued spherical fuzzy matrices. We develop methods for computing determinant and adjoint, and develop algorithms using composition functions to determine the greatest and least eigenvalue interval valued spherical fuzzy sets and create a flow chart to depict the procedure. In this paper, a new distance measure has been proposed and is to be proved valid by satisfying all the conditions of the distance metric. In addition, an application of interval-valued spherical fuzzy matrices to deal with decision-making problems is presented.