Abstract: The bi-level multiple followers linear programming with trapezoidal fuzzy decision variables model is firstly established in this paper, which is widely applied to multi-level management systems with hierarchical features. By using the fuzzy structured element theory, the ordering of trapezoidal fuzzy numbers is transformed into the ordering of monotone bounded functions through the fuzzy numbers structured element weighted order, and the model's optimal solution is proved to be equivalent to the optimal solution of the bi-level multiple followers linear programming model, and the effective algorithm is designed. Finally, two illustrative numerical examples are provided to demonstrate the feasibility of the proposed method.

Key words: bi-level linear programming, trapezoidal fuzzy number, fuzzy structure element, multiple followers