文档介绍：南京航空航天大学硕士学位论文
摘要
多属性决策是决策理论和现代科学决策的重要内容,广泛应用于工程设
计、社会生活、经济管理、军事等方面。多属性决策理论与方法的研究具有
重要的现实意义。
本文探讨了多属性决策的一些方法,主要成果如下:
(1)提出了一些基于简单加权法的多属性决策的灵敏度分析算法。首
先提出了一种新的当一个或多个属性权重扰动时其余权重变化的方法,同时
还讨论了当一个权重扰动时其余权重保持排序不变时的扰动范围;给出了一
种基于属性值规范化的情况下的属性值扰动界的算法;给出了当各方案的属
性值和属性权重都发生变化时,为使原方案的排序结果不变,属性权重和属
性值的一个扰动上界。
(2)讨论了有概率分布的区间数型多属性决策问题。列出了有概率分
布的区间数的运算公式。得出了两个密度函数是均匀分布的区间数四则运算
后不服从均匀分布的结论,并用仿真进行了证明。提出了一种新的区间数比
较大小方法,着重分析了密度函数是均匀分布和非均匀分布区间数的比较大
小,最后通过仿真对两种区间数比较大小的方法进行了比较,在此基础上提
出了有概率分布的区间数型多属性决策的一般计算方法。
(3)研究了给出方案偏好的多属性决策问题。针对方案的偏好值分别
为效用值、互反判断矩阵的情况,提出新的转换公式,建立模型,得到属性
权重值及方案的排序。
关键词:多属性决策,灵敏度分析,区间数,密度函数,判断矩阵
i
多属性决策的若干问题研究
ABSTRACT
Multiple attribute decision-making, which is one of the most important parts of
decision-making theory and modern decision-making science, is widely used in many
fields, such as engineering designs, society, economy, management, military affairs etc.
The main contents and achievements of this thesis are as follows:
In Chapter 2, sensitivity analysis for Multiple Attribute Decision Making is studied.
First, a new method about how other weights will change when one or some of the attribute
weights change is proposed, meanwhile the weight perturbation bounds of attribute which
keep the same sequence when the weight of one or some other attribute changes is also
discussed. Then, based on the standardized attribute values, an algorithm about the
perturbation bounds of each attribute value is given. At last the perturbation bounds of each
attribute value and attribute weight, which make the alternative maintain the same sort, are
obtained.
In Chapter 3, the mathematical operations formula of non-average interval number is
listed. And parison of interval number is put forward. Meanwhile, the results of two
methods pared by simulation.
In Chapter 4, a new method is put forward when only the decision maker’s preference
is given. A new conversion formula is proposed, and the sorting of the plans