摘要
论文较详细地论述了多属性决策中的有关问题,研究了多属性决策的一些重要的前沿内容——现有方法的改进与完善及新方法的提出、基于决策方法的权重确定、可化为区间信息表示的多属性决策方法和基于数据的区间数智能决策分析等。
具有创新性的主要研究成果包括以下几个方面:
(1)研究了模糊数与区间数的定义及他们之间的内在联系。提出了一种新的区间数距离测度,给出了区间数的二元运算关系,并对目前存在的多种区间数比较方法进行了比对,揭示了多种区间数比较方法之间的内在联系;综述了现有区间数决策矩阵的规范化方法,并对区间数向量进行了简要的介绍,总结了函数模型的决策与关系模型两类多属性决策方法,为本文进一步研究区间数不确定多属性决策方法的若干问题奠定了理论和实践基础;
(2)研究了基于区间数的扩展多属性决策方法。提出了基于区间数的多属性TOPSIS决策方法、VIKOR决策方法、α-PROMETHEE决策方法,并以某银行15家分支机构的经营状况的评估为例来比对分析上述方法;论述了权重值为区间数的区间数多属性决策方法,提出了权重值为区间数的区间数TOPSIS方法,并以在多属性MAS任务分配问题中的应用仿真实验来说明本文所提出的方法是有效且能够做出比较合理的任务分配决策;
(3)研究了基于区间数的多属性决策中权重确定。针对目前获得客观属性权重的方法多是在直接处理原始决策数据的基础上所得到的,决策所采用的方法在确定属性客观权重过程中则不起任何作用,本文用决策方法对原始决策数据进行预处理,再对处理后的数据探讨其属性的相对权重,即将决策方法与最终的权重确定相关联。根据这个思路,本文分析了属性加权向量ω与最终综合优先序值之间关系,提出了两种基于决策方法的属性客观权重ω的确定原理即基于区间数的PROMETHEE II方法中权重确定与基于投影寻踪模型的权重确定;
(4)研究了可化为区间数的多属性决策方法。把泛性模糊数及Vague集等其他模糊信息表示方式转化为区间数信息表示,提出了基于泛性模糊数的VIKOR多属性决策方法和基于Vague集的PROMETHEE方法。
(5)研究了基于数据的区间数智能决策分析。传统的决策分析是利用已有的信息建立函数或关系模型来进行决策,而随着计算机管理信息系统的飞速发展和广泛应用,社会经济和企业生产经营的规模和自动化水平不断提高,随之而来的是决策者面临的是大量的、动态的甚至是有噪声的信息,决策者企图通过建立函数或关系模型来进行决策显然是不可能的,也难于满足实际的需要。为此,本文扩展了一种基于区间数的FCM聚类算法,并提出了一种基于区间数的支持向量域多分类软计算方法,这两种基于知识的智能决策分析方法可以直接处理特征空间为区间数的聚类及多分类问题,扩宽了支持向量域多分类算法应用的范围。
This dissertation researches detailed relevant problems in MADM. Then, important contents of MADM: improvement on existing methods and presenting of new methods, determination on the attribute’s weights based on the method of decision making , the MACD for other information representation that it can be turned into interval numbers ,and the interval intelligent decision making based on data are studied thoroughly.
The innovative research findings are discussed as follows.
(1) The definition of interval numbers and fuzzy numbers and the intrinsic link between them are discussed in this thesis. It proposes a new distance measure for interval numbers and the binary operations for them are given too. Comparisons of interval numbers with existing methods are presented and it reveals the intrinsic link between different methods. Then a brief introduction is also demonstrated for the interval vector on the basis of a full review the existing methods of standardization for interval decision matrix. Next it sums up the function model and relational model of multiple attribute decision making and lays the foundation for further study uncertain decision making theory and method based on interval numbers.
(2) The uncertain decision making theory and method based on interval numbers are studied in the dissertation. It advances several methods such as TOPSIS, VIKOR,α-PROMETHEE for uncertain multiple attribute decision making based on interval numbers and a case study of comparing 15 bank branches in Iran was conducted to examine the applicability of these method. Then interval weight for uncertain decision making based on interval numbers are discussed and it proposes a TOPSIS methods dealing with interval weight for uncertain multiple attribute decision making based on interval numbers. And it works out a multi-attribute assignment problems in MAS to illustrate the method proposed by this article.
(3) The method of determining the attribute’s weights for uncertain decision making based on interval numbers are researched. Against the method of obtaining objective weight on the base of dealing directly with the original decision data currently and the method of decision making not play any role in the process, this paper preprocess firstly the original decision data with the method of decision making and determines the relative weight of attribute. According to the idea, this paper analyzes the relationship between the attribute’s weights and the synthetic priority value and advances two kinds of methods for determining the attribute’s weights based on the method of decision making, namely the weights determination based on extended PROMETHEE II method and projection pursuit model. This method is more suitable for the occasion of more schemes.
(4) Other information representation that it can be turned into interval numbers is presented in this dissertation. It brings forward the VIKOR method based on generalized fuzzy numbers and the PROMETHEE method based on vague sets on the foundation of the interval numbers translated from generalized fuzzy numbers and vague sets.
(5) The interval intelligent decision making based on data are researched. Traditional methods for decision analysis make use of the existing information to establish the function model or relation model; it is obviously not possible that the decision maker attempts to do it by establishing model with the rapid development and wide application of management information system, the increasing level of automation and the scale of production and operation for socio-economic and business, and more hard, dynamic even noise information. Therefore, this paper extends the FCM based on interval numbers for clustering algorithm, and propounds a multi-classification algorithm based on interval support vector machines. Both the knowledge-based intelligent decision analysis methods can work directly with characteristics of the space for the interval number for clustering and classification issues.
引文
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