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The interactive fuzzy programming approach can be used to address two-level programming problems if a mutually cooperative relationship exists between the decision-makers. In this approach, a satisfactory solution is obtained by taking into account the minimum satisfaction level of the decision-maker at the upper level. In addition, the overall satisfaction balance between the decision-maker at the lower level and the decision-maker at the upper level must be appropriate. In this paper, interactive fuzzy programming is used to achieve a satisfactory solution for a two-level linear programming problem with two decision-makers at the upper level. The method is designed in such a way that both decision-makers at the upper level achieve their minimum satisfaction levels together with the appropriate satisfaction balance between the decision-maker at the lower level and each decision-maker at the upper level. A numerical example is given to illustrate the method. Moreover, it is indicated that a three-level program can be considered as a two-level program with two decision-makers at the upper level.

Two-Level Linear Programming Problems with Two Decision-Makers at the Upper Level: An Interactive Fuzzy Approach