Interactive decision making for large-scale multiobjective linear programs with fuzzy numbers

In this paper, by considering the experts' imprecise or fuzzy understanding of the nature of the parameters in the problem-formulation process, large-scale multiobjective block-angular linear programming problems involving fuzzy numbers are formulated. Through the use of the α-level sets of fuzzy numbers, an extended Pareto optimality concept, called the α-Pareto optimality is introduced. To generate a candidate for the satisfactory solution which is also α-Pareto optimal, the decision maker is asked to specify the degree α and the reference objective values. It is shown that the corresponding α-Pareto optimal solution can be easily obtained by solving the minimax problems for which the Dantzig–Wolfe decomposition method is applicable. Then a linear programming-based interactive decision-making method for deriving a satisfactory solution for the decision maker efficiently from an α-Pareto optimal solution set is presented.