一种变量是梯形模糊数的两层多随从线性规划模型及其算法

Model and Algorithm of the Bi-level Multiple Followers Linear Programming with Trapezoidal Fuzzy Decision Variables

针对具有递阶特征的多层管理系统,本文建立了一种变量为梯形模糊数的两层多随处线性规划模型.利用模糊结构元理论,通过模糊数的结构元加权序,将梯形模糊数的排序转化为单调有界函数的排序,从而证明了该模型的最优解等价于两层多随处线性规划模型的最优解;进而提出了求解该模型的有效算法.最后,通过两个数值算例验证了该方法的可行性.

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.