A fuzzy satisficing method for large-scale linear-programming problems with block angular structure

In this paper, we focus on large-scale linear programming problems with block angular structure for which the Dantzig–Wolfe decomposition method has been successfully applied. By considering the vague nature of human judgements, we assume that the decision maker may have a fuzzy goal for the objective function and fuzzy constraints for the coupling constraints. Having elicited the corresponding linear membership functions through the interaction with the decision maker, if we adopt the convex fuzzy decision for combining them, it is shown that, under some appropriate conditions, the formulated problem can be reduced to a number of independent linear subproblems and the overall satisficing solution for the decision maker is directly obtained by solving the subproblems only.