一般二元关系的不确定性度量

发布时间：2018-04-13 11:37

本文选题：二元关系 + 不确定性　；参考：《渤海大学》2017年硕士论文

【摘要】：信息熵是不确定性度量的一个有效措施。中外著名学者已经提出了很多测量不确定性的方法,并取得了令人瞩目的成就,为我们获取有用的知识奠定了坚实的基础,并大大提高我们获取信息的效率。而关系是建立论域中一组元素之间联系的基本概念,集合和关系的定义是构成现代数学的基础。另外,关系已经被广泛应用于数据的离散化,模糊聚类和属性约简。关系中的等价关系、相似关系、邻域关系是粗糙集模型的基础。特殊关系的不确定性度量已有很多好的衡量方法,然而,一般二元关系不确定性的研究很少。因此本文主要针对一般二元关系间的不确定性进行研究。本文的总体思想是:将后继邻域,信息系统的基础知识和信息熵相结合,分别提出了一般二元关系熵,广义邻域熵,然后对它们的性质进行了详细的讨论,具体工作如下:1.为了计算一般二元关系熵,联合熵,条件熵和互信息,主要通过后继邻域对论域形成划分,从而来计算一般二元关系的熵、联合熵、条件熵和互信息,并提出了一些基本性质,然后与邻域熵进行比较,通过证明说明这两种熵的定义是等价的。2.在邻域熵的基础上,通过后继邻域重新定义了广义邻域熵,提出了广义邻域熵,条件熵,联合熵及互信等概念,并对它们的性质进行了讨论,最后与邻域熵进行比较,发现这是一种更全面,更精确的计算信息系统不确定性的一种熵。
[Abstract]:Information entropy is an effective measure to measure uncertainty.Famous scholars at home and abroad have put forward many methods to measure uncertainty, and have made remarkable achievements, which have laid a solid foundation for us to obtain useful knowledge and greatly improve the efficiency of our access to information.The relation is the basic concept of establishing the relation between a group of elements in the domain, and the definition of set and relation is the foundation of modern mathematics.In addition, relationships have been widely used in data discretization, fuzzy clustering and attribute reduction.The equivalence relation, similarity relation and neighborhood relation in relation are the basis of rough set model.There are many good methods to measure uncertainty of special relationships, however, there are few researches on uncertainty of binary relationships.Therefore, this paper mainly focuses on the uncertainty between general binary relations.The general idea of this paper is as follows: combining the basic knowledge and information entropy of subsequent neighborhood and information system, the general binary relation entropy and generalized neighborhood entropy are proposed, and their properties are discussed in detail. The specific work is as follows: 1.In order to calculate the general binary relation entropy, joint entropy, conditional entropy and mutual information, the entropy, joint entropy, conditional entropy and mutual information of the general binary relation are calculated by dividing the domain by the following neighborhood, and some basic properties are proposed.Then compared with the neighborhood entropy, it is proved that the definition of these two kinds of entropy is equivalent. 2.On the basis of neighborhood entropy, the generalized neighborhood entropy is redefined by successive neighborhood entropy. The concepts of generalized neighborhood entropy, conditional entropy, joint entropy and mutual trust are proposed, and their properties are discussed.It is found that this is a more comprehensive, more accurate calculation of information system uncertainty an entropy.
【学位授予单位】：渤海大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O236

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