Large Scale Fuzzy Linear Programming

This chapter treats large scale linear programming problems with block angular structures for which the Dantzig-Wolfe decomposition method has been successfully applied. Considering the vague or fuzzy nature of human judgments, both the fuzzy goal and fuzzy constrains of the decision maker are introduced. Having determined the corresponding membership functions, following the convex fuzzy decision for combining them, under suitable conditions, it is shown that the formulated problem can be reduced to a number of independent linear subproblems and the satisficing solution for the decision maker is directly obtained just only by solving the subproblems. Moreover, even if the appropriate conditions are not satisfied, it is shown that the Dantzig-Wolfe decomposition method is applicable.