A Compromise Solution for the Neutrosophic Multiobjective Linear Programming Problem and its Application in Transportation Problem

Neutrosophic set theory plays an important role in dealing with the impreciseness and inconsistency in data encountered in solving real-life problems. The current paper focuses on the Neutrosophic Fuzzy Multi-Objective Linear Programming Problem (NFMOLPP), where the coefficients of the objective functions, constraints and right-hand side parameters are single-valued trapezoidal Neutrosophic Numbers (NNs). From the viewpoint of complexity of the problem, a ranking function of NNs is proposed to convert the problem into equivalent MOLPPs with crisp parameters. Then suitable membership functions for each objective are formulated using their lowest and highest value. With the aim of linear programming techniques, a compromise optimal solution of NFMOLPP is obtained. The main advantage of the proposed approach is that it obtains a compromise solution by optimizing truth-membership, indeterminacy-membership, and falsity-membership functions, simultaneously. Finally, a transportation problem is introduced as an application to illustrate the utility and practicality of the approach.