弃权影响下Vague集相似性度量方法的改进及应用

发布时间：2018-02-03 06:44

本文关键词： Vague集(值) 相似性度量区分度 TOPSIS法动态信息集结法　出处：《西安科技大学》2017年硕士论文　论文类型：学位论文

【摘要】：近年来,Vague集的相似性度量方法以及基于Vague集的多属性决策方法的研究受到了国内外学者的高度关注。1993年,Gau和Buehrer提出了处理模糊信息的理论—Vague集理论,该理论本质是对Fuzzy集理论的扩展。本文依据已有的几种Vague集的相似性度量方法的思想并考虑到弃权部分对Vague集相似性度量的影响,通过对改进的相似性度量方法的证明和实验数据的分析,探讨了改进后的相似性度量方法对数据区分的影响,在此基础上将改进的相似性度量方法应用到多属性决策之中,通过具体的实例分析给出了合理的决策结果。主要内容如下:首先,介绍了Vague集的相似性度量的相关理论,即Vague集的相似性度量的定义、运算以及性质等,分析了构造Vague集的相似性度量方法需满足的条件、定理。在此基础上分析了已有的几种Vague集的相似性度量方法,针对已有相似性度量方法未考虑到弃权部分对Vague集相似性度量的影响以及对数据不能进行有效区分的缺点,提出了改进的相似性度量方法以及改进的加权相似性度量方法。对改进的相似性度量方法的定义的完备性在理论上进行了证明,并通过九组随机实验数据分析改进的相似性度量方法对数据的影响,为了进一步扩大数据的范围,分别在区间[0,1]上找到以0.1为步长的36*36组数据和以步长为0.01的2602*2602组数据对几种度量方法进行了分析、比较,可得出改进的相似性度量方法对数据的区分度更有效、更高。其次,由于多属性决策问题存在不确定性,将Vague集理论与多属性决策的问题相结合,使得多属性决策问题的解决更加快捷、有效。通过对基于Vague集理论的多属性决策算法步骤的分析,针对备选方案的排序是直接影响决策结果的重要因素,为了能对备选方案进行合理的区分,本文选取了改进的Vague集的相似性度量公式作为多属性决策问题的记分函数。最后,通过改进的Vague集的相似性度量方法在简单加权法、TOPSIS法和动态信息集结方法上的应用,即对具体的实例进行分析,并给出了合理的决策结果。
[Abstract]:In recent years, the research on similarity measurement of vague sets and multi-attribute decision making based on Vague sets has been highly concerned by scholars at home and abroad. In 1993. Gau and Buehrer put forward the theory of dealing with fuzzy information-vague set theory. The essence of this theory is to extend the Fuzzy set theory. According to the idea of several existing similarity measurement methods of Vague sets and considering the influence of waiver part on the similarity measurement of Vague sets. Through the proof of the improved similarity measurement method and the analysis of the experimental data, the influence of the improved similarity measurement method on the data differentiation is discussed. On this basis, the improved similarity measurement method is applied to multi-attribute decision making, and a reasonable decision result is given through concrete examples. The main contents are as follows: first. This paper introduces the theory of similarity measurement of Vague sets, that is, the definition, operation and properties of similarity measurement of Vague sets. The conditions and theorems needed to be satisfied in constructing the similarity measurement methods of Vague sets are analyzed. On this basis, several existing similarity measurement methods of Vague sets are analyzed. The existing similarity measurement methods do not take into account the impact of waiver on similarity measurement of Vague sets and the disadvantage that data can not be effectively distinguished. An improved similarity measurement method and an improved weighted similarity measurement method are proposed. The completeness of the definition of the improved similarity measurement method is proved theoretically. The influence of the improved similarity measurement method on the data is analyzed through nine groups of random experimental data. In order to further expand the range of the data, [In this paper, 36 groups of data with 0.1 step size and 2602 groups of data with step size 0.01 were found to analyze and compare several measurement methods. It can be concluded that the improved similarity measurement method is more effective and higher in data differentiation. Secondly, because of the uncertainty of multi-attribute decision making problem, the Vague set theory is combined with the multi-attribute decision making problem. The solution of multi-attribute decision making problem is faster and more effective. Through the analysis of the steps of multi-attribute decision making algorithm based on Vague set theory. The ranking of alternatives is an important factor that directly affects the decision results, in order to make a reasonable distinction between the alternatives. In this paper, the improved Vague set similarity measurement formula is selected as the score function of the multi-attribute decision making problem. Finally, the simple weighting method is used to measure the similarity of the improved Vague set. The application of TOPSIS method and dynamic information aggregation method is the analysis of concrete examples and the reasonable decision results are given.
【学位授予单位】：西安科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159

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