含直觉模糊弹性约束的广义模糊变量线性规划

doi:10.12005/orms.2016.0208

运筹与管理 ›› 2016, Vol. 25 ›› Issue (6): 105-111.DOI: 10.12005/orms.2016.0208

含直觉模糊弹性约束的广义模糊变量线性规划

张京亮¹, 陈之宁²

1.陆军军官学院研究生二队,安徽合肥 230031;
2.陆军军官学院基础部数学教研室,安徽合肥 230031

出版日期:2016-12-20
作者简介:张京亮(1989-),男,硕士研究生,研究方向:模糊数学与数据分析;陈之宁(1963-),男,教授,硕士生导师,研究方向:模糊数学与决策等。

Generalized Fuzzy Variable Linear Programming withIntuitive Fuzzy Elastic Constraints

ZHANG Jing-liang¹, CHEN Zhi-ning²

1.Brigade of Postgraduate, Army Officer Academy of PLA, Hefei 230031, China;
2.Staff Room of Mathematics, Department of Basic Theories, Army Officer Academy of PLA, Hefei 230031, China

Online:2016-12-20

摘要/Abstract

摘要： 本文基于模糊结构元方法建立并讨论了一类含有直觉模糊弹性约束的广义模糊变量线性规划问题。首先,简单介绍了结构元方法并对结构元加权排序中权函数表征决策者风险态度进行了深入分析。然后,通过选取风险中立型决策态度来定义序关系并拓展Verdegay模糊线性规划方法,将新型模糊变量线性规划问题转化为两个含一般模糊弹性约束的模糊变量线性规划模型,给出了此类规划最优直觉模糊解的求法。最后,通过数值算例进一步说明该方法的有效性。

关键词: 模糊变量, 模糊结构元, 风险态度, 直觉模糊弹性约束, 最优直觉模糊解

Abstract: In this paper, a class of new fuzzy variable linear programming problem with intuitionistic fuzzy elasticconstraints is constructed and discussed based on the fuzzy structured element method. Firstly, the authors introduce the basic principle of structured element and make an analysis of the connection between weight function and risk attitude of decision-makers. Then, by choosing the risk neutral decision attitude to define an order relation and expanding Verdegay’s fuzzy linear programming method, the authors transform the new fuzzy variable linear programming problem into two general fuzzy variable linear programming with fuzzy elastic constraints .The intuitionistic optimal solution of the two general fuzzy variable linear programming with fuzzy elastic constraints is given. Finally, the authors further illustrate the effectiveness of this method by a numerical example.

Key words: fuzzy variables, fuzzy structured element, risk attitude, intuitionistic fuzzy elastic constraints, intuitionistic fuzzy optimal solution

中图分类号:

O159
O221.1

张京亮, 陈之宁. 含直觉模糊弹性约束的广义模糊变量线性规划[J]. 运筹与管理, 2016, 25(6): 105-111.

ZHANG Jing-liang, CHEN Zhi-ning. Generalized Fuzzy Variable Linear Programming withIntuitive Fuzzy Elastic Constraints[J]. Operations Research and Management Science, 2016, 25(6): 105-111.

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含直觉模糊弹性约束的广义模糊变量线性规划

Generalized Fuzzy Variable Linear Programming withIntuitive Fuzzy Elastic Constraints

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