论文标题:模糊数排序及模糊线性规划
Fuzzy Number Ranking and Fuzzy Linear Programming
论文作者
论文导师 刘琼荪,论文学位 硕士,论文专业 应用数学
论文单位 重庆大学,点击次数 131,论文页数 59页File Size553K
2007-10-01论文网 http://www.lw23.com/lunwen_72951882/
Fuzzy set;; Fuzzy number;; Fuzzy linear programming with elastic constrains;; Linear programming with coefficients;; Centroid point of fuzzy number;; Dual problem
在现实生活和工程领域中,存在着许多不确定现象,这种不确定现象主要表现为随机性、模糊性和粗糙性。而在数学规划中,这种不确定现象会给决策者带来较大困难。本文主要对模糊数及不确定规划中的模糊线性规划作了较为深入的分析与讨论。由于模糊数排序在模糊优化中的重要作用,本文首先介绍了模糊数的概念及基本运算性质。对模糊数排序的经典方法作了简要的介绍,同时引入了模糊数中心的概念,并提出了以模糊数中心为基础的模糊数排序方法来弥补前人提出的此类方法的不足。 其次,本文详细介绍了两类模糊线性规划:带模糊约束的线性规划及模糊系数线性规划问题,分析了这两类规划的解决方法。对带模糊约束的线性规划问题,本文在Werners提出的方法基础上进行了改进,得到一种新的求解方法。从理论上,我们证明了该方法得到的解具有模糊有效性,并用实例进行了验证。关于模糊系数线性规划问题,本文引入了模糊关系,在此基础之上提出了解的可行度概念,并讨论了解的可行度与最优值的满意度之间的关系,在综合考虑到两者平衡的基础上对模糊系数线性规划提出了新的求解方法。 由于对偶理论在线性规划中具有重要的作用,本文也简单考虑了关于模糊线性规划的对偶问题。在带模糊约束线性规划的求解方法基础上,提出了它的对偶问题的形式及相关的定理。
In real life and engineering fields, there are many uncertain phenomena, whose main performances are randomness, fuzziness and roughness. But in mathematic programming, these kinds of uncentain phenomena bring difficulties to the policy makers. This paper mainly analyses the relevant contents of fuzzy number and fuzzy linear programming, which pertain to uncertain programming. For fuzzy number plays an important role in fuzzy programming, we introduce the concept of fuzzy number firstly and then present the classic methods of ranking fuzzy number. Then the centroid point of fuzzy number is introduced in chapter three. Meanwhile, we propose a new method in fuzzy number raking based on the centroid point to overcome the shortcoming of the method proposed formerly. Secondly, we introduce two kinds of fuzzy programming: fuzzy linear programming with ilastic constrains and linear programming with fuzzy coefficients. In chapter four, we analyse mehtods to solve both programmings. For the former problem, this paper proposes a new solution, which is improved based on the Max-min method proposed by Werners. The result of the new method is fuzzy efficient in theory. Moreover, an example is given to illustrate the solution is efficient under the new model. Concerning the latter programming, we propose the concept of feasibility degree and satisfaction degree to the solution based on a special fuzzy relation and ranking function respectively. Then we discuss the relation between the feasibility degree and satisfaction degree. After consideration of the balance of both concepts, we bring forward a new way to solve the kind of fuzzy linear programming. Owing to the important function of dual theory in linear programming, we discuss the dual problem to the fuzzy linear programming with elastic constrains. Based on the usual sulotion of the problem, we give the form of dual problem of the fuzzy linear programming. Finally, we give a theorem about it.
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