Interactive decision-making for multiobjective linear fractional programming problems with block angular structure involving fuzzy numbers

Abstract In this paper, by considering the experts' vague or fuzzy understanding of the nature of the parameters in the problem-formulation process, multiobjective linear fractional programming problems with block angular structure 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 satisficing 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 and Ritter's partitioning procedure are applicable. Then a linear programming-based interactive decision-making method with decomposition procedures for deriving a satisficing solution for the decision maker efficiently from an α-Pareto optimal solution set is presented. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method.