quadratic bi-level programming problems: a fuzzy goal programming approach

this paper presents a fuzzy goal programming (fgp) methodology for solving bi-level quadratic programming (blqp) problems. in the fgp model formulation, firstly the objectives are transformed into fuzzy goals (membership functions) by means of assigning an aspiration level to each of them, and suitable membership function is defined for each objectives, and also the membership functions for vector of fuzzy goals of the decision variables controlled by decision maker at the first level are developed in the model formulation of the problem. to achieve the highest membership value of each of the fuzzy goals, we formulate the problem by minimizing the negative deviational variables and thereby obtaining the most satisfactory solution for all decision makers. a numerical example is given to demonstrate the proposed approach.