An interactive fuzzy satisficing method for large-scale multiobjective linear programming problems with block angular structure

In this paper, the authors present an interactive fuzzy satisficing method for large-scale multiobjective linear programming problems with the block angular structure. By considering the vague nature of human judgements, they assume that the decision maker (DM) may have a fuzzy goal for each of the objective functions. Having elicited the corresponding linear membership functions, if the DM specifies the reference membership levels for all the membership functions, the corresponding Pareto optimal solution which is, in the minimax sense, nearest to the requirement or better than that if the reference membership levels are attainable can be obtained by solving the minimax problem. Here it is shown that the formulated minimax problem can be reduced to one master problem and a number of linear subproblems and the Pareto optimal solution together with the trade-off rate information between the membership functions can be obtained by applying the Dantzig-Wolfe decomposition method. In this way, the satisficing solution for the DM can be derived from Pareto optimal solutions by updating the current reference membership levels on the basis of the current levels of the membership functions together with the trade-off rates between the membership functions.