求解上层含约束条件且具有模糊决策变量二层线性规划的结构元方法

Solving Bilevel Linear Programming with Upper Constraint and Fuzzy Decision Variables through Structured Element Method

讨论一类含模糊决策变量二层线性规划模型,利用模糊结构元理论,证明该模型最优解等价于二层线性规划模型最优解,并通过极点搜索法得到该模型最优解,最后通过数值算例验证该方法的可行性。

Bilevel linear programming with upper constraint and fuzzy decision variables, a typical model optimal solution, is proved to be equivalent to the optimal solution of the bilevel linear programming model by using fuzzy structured element theory in this paper. By using the vertex enumeration approach, the optimal solution of the bilevel linear programming model is found out. Finally, an illustrative numerical example for the bilevel linear programming with fuzzy decision variables model is provided to demonstrate the feasibility and efficiency of the proposed method.