Interactive fuzzy programming for multilevel linear programming problems with fuzzy parameters

This paper considers the multilevel linear programming problem with fuzzy parameters, and proposes an interactive fuzzy programming method. Lai and colleagues recently proposed a fuzzy programming method for the multilevel linear programming problem, but there remained the possibility that the procedure could arrive at an undesirable solution. This paper is an attempt to cope with this problem. Extending the multilevel linear programming problem to the problem with fuzzy parameters, an interactive fuzzy programming method is proposed as follows. The fuzzy goal is defined for the objective function of the decision-maker of each level. The decision-maker except for the lowest level subjectively defines the minimum tolerance for satisfaction. Then, by considering the satisfaction ratio among the levels and interactively updating the minimum tolerance of the decision-maker, if necessary, the satisficing solution is efficiently derived, while considering the intention of the decision-makers at the upper level as well as the balance of the achieved satisfactions among the levels. Lastly, a numerical example is investigated for the three-level linear programming problem with fuzzy parameters, and the validity and effectiveness of the proposed method are demonstrated. (C) 2000 Scripta Technica.