求解多层线性规划的模糊规划法

运筹学学报 ›› 2011, Vol. 15 ›› Issue (4): 85-92.

求解多层线性规划的模糊规划法

宋伟, 赵茂先, 王向荣

1. 山东省汶上县郭楼镇卫生院
2. 山东科技大学信息科学与工程学院
3.

收稿日期:2010-12-15 修回日期:2011-05-26 出版日期:2011-12-15 发布日期:2011-12-19
通讯作者: 宋伟 E-mail:songwei3614@126.com

Fuzzy programming approach for Multilevel linear programming

SONG Wei, ZHAO Mao-Xian, WANG Xiang-Rong

Received:2010-12-15 Revised:2011-05-26 Online:2011-12-15 Published:2011-12-19

摘要/Abstract

摘要： 本文用模糊集理论中的隶属函数描述多层线性规划的各层目标，在第一层给定最小满意水平下，通过求解相应层次的模糊规划来确定各层的最小满意度，从而最终得到问题的一个满意解。提出的方法只需求解一系列线性规划问题，具有较好的计算复杂性和可行性，最后的算例进一步验证了方法的有效性。

关键词: 多层线性规划, 模糊规划, 隶属函数, 满意解

Abstract: In this paper, membership functions of fuzzy set theory described each objective of multilevel linear programming, after the first decision-maker gives a minimum satisfaction level, by solving the corresponding levels of fuzzy programming to determine the minimum satisfaction degree of each level, and ultimately gets a satisfactory solution of the problem. The proposed method only needs to solve a series of linear programming problems, with better complexity and feasibility, the last example further verifies the validity of the method.

Key words: Multilevel linear programming, fuzzy programming, membership functions,
satisfactory solution

宋伟, 赵茂先, 王向荣. 求解多层线性规划的模糊规划法[J]. 运筹学学报, 2011, 15(4): 85-92.

SONG Wei, ZHAO Mao-Xian, WANG Xiang-Rong. Fuzzy programming approach for Multilevel linear programming[J]. Operations Research Transactions, 2011, 15(4): 85-92.