Optimal Solution for Fully Spherical Fuzzy Linear Programming Problem

This study presents an innovative extension to existing fuzzy set models, introducing the concept of spherical fuzzy sets.Distinguished by their three function characteristics-positive, neutral, and negative membership degrees-the sum of their squares is constrained to be no more than one.This paper discusses the application of these sets through the lens of fully fuzzy spherical linear programming problems, where spherical fuzzy numbers are utilized as parameters.A crisp version of the Spherical Fuzzy Linear Programming Problem (SFLPP) is generated by leveraging these membership degrees.A novel method is proposed for the de-fuzzification of spherical fuzzy numbers into crisp interval numbers.Further, the Best Worst Method (BWM) is employed to solve the crisp Linear Programming Problem (LPP).Alongside this, we propose a spherical fuzzy optimization model to resolve the SFLPP.The validity and optimality of our proposed methodology are substantiated with a detailed numerical example.