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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2021, Vol. 38 ›› Issue (1): 49-62.doi: 10.3969/j.issn.1005-3085.2021.01.005

• • 上一篇    下一篇

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

周喜华1,  贾洪信1,  黄晓红1,   邓胜岳2,  谢   亮2   

  1. 1- 广东环境保护工程职业学院基础教育部，佛山 528216
    2- 湖南工业大学理学院，株洲 412007
  • 收稿日期:2018-09-05 接受日期:2019-10-23 出版日期:2021-02-15 发布日期:2021-04-15
  • 通讯作者: 邓胜岳 E-mail: dsy110@163.com
  • 基金资助:
    湖南省自然科学基金 (2019JJ50125; 2020JJ4264)；湖南省教育厅科研项目 (16C0515; 20B180)；广东省数学会高职高专教师教育科研项目 (GDGZSX2019007)；全国职业教育科研规划项目 (2019QZJ045).

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

ZHOU Xi-hua1,   JIA Hong-xin1,   HUANG Xiao-hong1,   DENG Sheng-yue2,   XIE Liang2   

  1. 1- Department of Foundation Courses, Guangdong Polytechnic of Environmental Protection Engineering, Foshan 528216
    2- School of Science, Hunan University of Technology, Zhuzhou 412007
  • Received:2018-09-05 Accepted:2019-10-23 Online:2021-02-15 Published:2021-04-15
  • Contact: S. Deng. E-mail address: dsy110@163.com
  • Supported by:
    The Natural Science Foundation of Hunan Province (2019JJ50125; 2020JJ4264); the General Project of Hunan Provincial Education Department of China (16C0515; 20B180); the Research Program for Vocational College Teachers' Education of Guangdong Mathematics Association (GDGZSX2019007); the National Vocational Education Research Planning Project (2019QZJ045).

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摘要： 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．

关键词: 两层线性规划, 梯形模糊数, 模糊结构元, 多随从

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

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