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.