模糊聚类分析算法研究.doc

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摘要
聚类就是按照事物间的相似性进行区分和分类的过程，在这一过程中没有教师指导，因此是一种无监督的分类。聚类分析则是用数学方法研究和处理所给定对象的分类。传统的聚类分析是一种硬划分，它把每个待辨识的对象严格地划分到某个类中，具有非此即彼的性质，因此这种分类的类别界限是分明的。而实际上大多数对象并没有严格的属性，它们在性态和类属方面存在着中介性，适合进行软划分。Zadeh提出的模糊集理论为这种软划分提供了有力的分析工具，人们开始用模糊的方法来处理聚类问题，并称之为模糊聚类分析。
模糊聚类分析算法的一般包括三个步骤:第一步:数据标准化;第二步:建立模糊相似矩阵;第三步:聚类。本文对模糊聚类分析中的两种算法进行了重点研究。最后利用matlab实现了一个模糊聚类算法，并用实例加以验证。
关键词：模糊集合，模糊聚类分析，模糊等价矩阵，传递闭包
Abstract
This paper will illustrate “clustering analysis” thoroughly. Cluster is a process that assorts things by their similarity. There is no adviser in this process, so it is a non-supervised classification. “Clustering analysis” research and process assort things by mathematical means. Traditional Clustering analysis assorts things strictly: therefore the limit of the classification is very clearly. But in fact most of the things have no obvious attribute by each: their limit is vague, as a result soft classification is a better way to process them. Professor Zadeh introduced the theory of fuzzy sets, which offer a powerful means to solve the problem. People begin to use fuzzy way to deal with clustering problem, and call it “fuzzy clustering analysis”.
“Fuzzy clustering analysis” contains three steps. The first is data standardization; the second is to establish fuzzy similar matrix; the third is clustering. This paper will research two arithmetic of the Fuzzy clustering analysis. Finally, the paper will accomplish Fuzzy clustering analysis program by matlab. It is significant to use data to validate it.
Key words: fuzzy set, fuzzy clustering analysis, fuzzy equivalent matrix, transitive closure

目录
HYPERLINK \l "_Toc" 第1章 引言 1
HYPERLINK \l "_Toc" 1
HYPERLINK \l "_Toc" 3
HYPERLINK \l "_Toc" 3
HYPERLINK \l "_Toc" 第2章 模糊聚类分析综述 4
HYPERLINK \l "_Toc" 4
HYPERLINK \l "_Toc" 模糊集合的表示法 4
HYPERLINK \l "_Toc" 模糊集的运算及性质 5
HYPERLINK \l "_Toc" 模糊集的