一类变量为梯形模糊数的两层线性规划模型及其算法  

Bi-Level Linear Programming Model and Algorithm with Trapezoidal Fuzzy Numbers for a Class of Variable

作　　者：周喜华 黄晓红 邓胜岳[2] 刘玮 ZHOU Xi-hua;HUANG Xiao-hong;DENG Sheng-yue;LIU Wei(Guangdong Polytechnic of Environmental Protection Engineering,Foshan 528216,China;School of Science,Hunan University of Technology,Zhuzhou 412007,China)

机构地区：[1]广东环境保护工程职业学院公共课教学部,广东佛山528216 [2]湖南工业大学理学院,湖南株洲412007

出　　处：《数学的实践与认识》2024年第6期175-185,共11页Mathematics in Practice and Theory

基　　金：湖南省自然科学基金(2016JJ2043);2022年广东省职业院校实习指导工作委员会项目(职业院校实习课程思政推进路径研究——以专升本高等数学为例)。

摘　　要：针对一类变量为梯形模糊数的两层线性规划,首先根据模糊结构元理论,利用有界实模糊数与[-1,1]上的标准单调有界函数是一一对应的关系,将梯形模糊数的排序转化为对应的单调函数的排序,从而定义了梯形模糊数的结构元加权序;其次,证明了一类变量为梯形模糊数的两层线性规划的最优解等价于两层线性规划的最优解,并且两层线性规划在约束集为非空有界的条件下,该模型的可行集具有弱拟凸性和连通性,再利用KKT条件得到了两层线性规划的最优化条件,并设计了有效算法;最后,两个算例验证了该方法的有效性和可行性.Fuzzy bi-level linear programming is a combination of fuzzy mathematics and bi-level linear programming studying a bi-level linear programming model with trapezoidal fuzzy numbers.According to the fuzzy structured element theory,there is an one-to-one correspondence relationship between bounded real fuzzy numbers and standard monotonic bounded function in[-1,1],getting the conclusion that the order between fuzzy numbers can be converted to the order between monotonic functions,then defining the structured element's weighted order of fuzzy numbers,and proving that the optimal solution of an bi-level linear programming problem with trapezoidal fuzzy numbers is equivalent to the optimal solution of an bi-level linear programming problem.On the premise of bi-level linear programming's constrained set is nonempty and bounded,the feasible set is both a weak quasi-convex set and connected set,then getting the most optimistic condition of BLP problem by duality theory,then transforming the bi-level linear programming problem to linear programming problem,finally solve the linear programming problem by MATLAB programming.

关 键 词：模糊结构元 梯形模糊数 两层线性规划 

分 类 号：O159[理学—数学]