基于聚类算法的区间型多属性大群体决策方法

发布时间：2018-04-03 00:19

本文选题：聚类算法　切入点：大群体　出处：《湖南理工学院》2017年硕士论文

【摘要】：由于经济问题的复杂化,越来越多的决策成员参与其中,群体规模逐渐扩大,现有的群决策方法已经不能满足需求。决策问题的不确定性与复杂化,也决定了决策者的评价信息也必须从多个属性出发,在此同时,由于人类思维的模糊性和不确定性,决策者的评价信息多数为模糊数,区间数尤为简单且常见,但目前对区间型多属性大群体决策研究还较少。本文针对属性权重信息完全已知和属性值为区间型随机变量的多属性大群体决策问题,提出了一种大群体决策方法。本文主要研究工作如下:首先,针对传统K-均值聚类算法对初始聚类中心的依赖性,提出了优选初始聚类中心的改进K-均值聚类算法。在考虑数据集实际分布的基础上,选择与实际聚类中心接近的样本点作为初始聚类中心,结果显示,在经过较少的迭代就可以得到稳定、准确率较高的聚类结果。然后,本文提出了区间型数据相似性度量标准,通过数学证明能满足相似度的基本性质,适合任意分布的区间数之间的相似性度量。在此基础上,本文结合改进K-均值聚类算法对区间型多属性大群体决策问题聚类分析,得到较好的聚类结果,证明了本文相似度定义式是有效的。其次,本文在对大群体数据聚类过程中,对比不同类别数情况下得到的聚类效果,由于类内相似度越大,同时类间相似度越小,聚类效果越好。因此计算类内与类间相似度比值,选择比值最大的类别数作为最佳聚类类别数。最后,本文对类权重的设定时,考虑了区间数据存在不确定性,以及群决策中以最大满意度为目标,提出与类权重密切相关的三个因素:区间宽度、类内评价信息的紧致性、类成员比重。相比于其他权重赋值方法,本文赋权方法更科学,更全面。
[Abstract]:Due to the complication of economic problems, more and more decision making members participate in it, and the group size is gradually expanded. The existing group decision making methods can not meet the demand.The uncertainty and complexity of the decision making problem also decide that the evaluation information of the decision maker must also proceed from many attributes. At the same time, due to the fuzziness and uncertainty of human thinking, most of the evaluation information of the decision maker are fuzzy numbers.Interval number is especially simple and common, but there are few researches on interval type multi-attribute large group decision making.In this paper, a large group decision making method is proposed to solve the problem of large group decision making in which the attribute weight information is completely known and the attribute value is interval random variable.The main work of this paper is as follows: firstly, an improved K-means clustering algorithm is proposed to optimize the selection of initial clustering centers in view of the dependence of the traditional K-means clustering algorithm on the initial clustering centers.On the basis of considering the actual distribution of the data sets, the sample points close to the actual clustering centers are selected as the initial clustering centers. The results show that the clustering results are stable and accurate after fewer iterations.Then, this paper presents the similarity measure standard of interval data. It is proved by mathematics that it can satisfy the basic properties of similarity degree and is suitable for the similarity measure between interval numbers with arbitrary distribution.On this basis, this paper combines the improved K-means clustering algorithm to cluster analysis of multi-attribute large group decision making problem with interval type, and obtains a better clustering result, which proves that the similarity definition in this paper is effective.Secondly, in the process of large group data clustering, compared with the different categories of the results of clustering, because the greater the intra-class similarity, at the same time, the smaller the similarity between the clusters, the better the clustering effect.Therefore, the ratio of intra-class similarity and inter-cluster similarity is calculated, and the number of categories with the largest ratio is selected as the best cluster number.Finally, considering the uncertainty of interval data and the goal of maximum satisfaction in group decision making, this paper proposes three factors closely related to class weight: interval width, compactness of in-class evaluation information.Class member specific gravity.Compared with other weight assignment methods, this method is more scientific and comprehensive.
【学位授予单位】：湖南理工学院
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP311.13;O225

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