Solving the general fully neutrosophic multi-level multiobjective linear programming problems

This paper addresses the general fully neutrosophic multi-level multiobjective programming problems i.e. ML-MOLPPs in which not only coefficients of each objective at each level but also all coefficients and parameters in the constraints are fully neutrosophic numbers in the form of trapezoidal neutrosophic numbers (NNs). From the point of view of complexity of the problem, it is proposed to apply ranking function of NNs to convert problem into equivalent ML-MOLPPs with crisp values of neutrosophic coefficients and parameters. Then suitable membership function for each objective and decision variable are formulated using lowest and highest value of each objective and decision variables of converted ML-MOLPP. Formulation of membership functions for decision variables (using corresponding values to maximum and minimum of objectives) will avoid decision deadlock in hierarchical structure. Accordingly, simple fuzzy goal programming strategy is applied to build FGP solution models. With the help of linear programming techniques on these solution models, compromise optimal solution of original fully neutrosophic ML-MOLPP is obtained. The proposed approach is a unique and simple method to provide compromise optimal solution to decision makers of general fully neutrosophic ML-MOLPP. The proposed approach is illustrated with numerical example to show its uniqueness and simplicity as solution technique. A case study is also discussed to demonstrate its applicability on real problems.