Spherical Fuzzy Multiobjective Linear Programming Problem

Abstract

Multiobjective optimization techniques are an essential and burning topic for the last few decades. The significant development can be realized by having enormous researches in this field, such as the fuzzy technique, an intuitionistic fuzzy optimization technique, different goal programming techniques, etc. Thus this chapter investigates a new algorithm based on the spherical fuzzy set (SF) named as the spherical fuzzy multiobjective programming problem (SFMOLPP) under the spherical fuzzy environment. The SFMOLPP inevitably involves the degree of neutrality along with positive and negative membership degrees of the element into the feasible solution set. It also generalizes the decision set by imposing the restriction that the sum of squares of each membership function must be less than or equal to one. The attainment of achievement function is determined by maximizing the positive membership function and minimization of neutral and negative membership function of each objective function under the spherical fuzzy decision set. At last, numerical examples and the conclusion are presented to reveal the applicability and future research scope in the SF domain.