Neutrosophic goal programming approach for multi-objective fixed-charge transportation problem with neutrosophic parameters

In real-life optimization problems, due to some uncertainty and hesitancy, it might be challenging for the decision-makers to identify the precise values of the parameters. To define this uncertainty, neutrosophic set theory is an extension of the crisp, fuzzy and the intuitionistic fuzzy set theory in which along with the incomplete information, indeterminate and inconsistent information is also handled. Considering these advantages, a model for the multi-objective fixed-charge transportation problem with the single-valued trapezoidal neutrosophic numbers is formulated here. To derive the Pareto-optimal solution for the presented model, neutrosophic goal programming approach is proposed which is rooted in the principles of maximizing the degree of satisfaction, maximizing the degree of indeterminacy and minimizing the degree of dissatisfaction. For demonstrating the applicability of the proposed approach, a numerical problem within the same framework is solved. Furthermore, the same problem is also solved using the fuzzy programming and intuitionistic fuzzy programming approach and a comparative analysis is conducted. The results demonstrate that the proposed neutrosophic goal programming approach consistently provides better Pareto-optimal solution as compared to the existing approaches. Finally, the implications of this research and outline avenues for the future research are also discussed at the last.