A novel approach for multi-objective linear programming model under spherical fuzzy environment and its application

Abstract

Every decision-making process particularly those involving real-life issues is disproportionately plagued by uncertainty. It is also unavoidable and obvious. Since its conception are several ways for representing uncertainty have been proposed by numerous academics to cope with uncertainty. Fuzzy sets and hierarchical such as picture fuzzy sets stand out among them as excellent representation techniques for modeling uncertainty. However, there are several significant drawbacks to the current uncertainty modeling techniques. Due to its vast versatility and benefits we here embrace the idea of the spherical fuzzy set, an extension of the picture fuzzy set. On the other hand amid uncertainty in real life the multi-objective plays a critical role. In this research paper determining a Multi-Objective Linear Programming Problem of Spherical fuzzy sets serves to stimulate nous. The score function corresponding to the degree positive, negative and neutral is the foundation upon which the suggested approach is developed. Additionally we apply the suggested strategy to the solution of the multi-objective linear programming problem to demonstrate its superiority through certain numerical examples. Maximization or Minimizing of the cost is the primary goal of the multi-objective linear programming problem. Using an explicitly defined score function the suggested solution transformed the Spherical Fuzzy Multi-Objective Linear Programming Problem into a Crisp Multi-Objective Linear Programming Problem (CMOLPP). We establish some theorems to show that the efficient solution of CMOLPP is likewise an efficient solution of SFMOLPP. The CMOLPP is then further simplified into a single-objective Linear Programming Problem (LPP) thus we revamp the modified Zimmermann’s approach in the environment of a nonlinear membership function with the aid of the suggested technique. It is possible to simply solve this single-objective LPP using any software or standard LPP algorithm. The suggested approach achieves the fuzzy optimum result without altering the nature of the issue. An application of the suggested approach has been used to illustrate it and its results have been distinguished from those of other preexisting methods found in the literature. To determine the importance of the suggested technique which adjudicate thorough theorem and result analysis is conducted.