一般模糊关系的不确定性度量

发布时间：2018-03-01 15:43

本文关键词： 模糊二元关系不确定性度量信息熵信息粒子　出处：《渤海大学》2017年硕士论文　论文类型：学位论文

【摘要】：关系是刻画元素之间相互联系的一个重要概念,关系被广泛应用在学术智能领域,例如,关系数据库,聚类分析,近似推理,属性约简,分类和决策。近年来一些特殊关系的不确定性度量用信息熵来表示。然而到目前为止,还没有一个系统的方法将这些不确定性度量构建成一个理论框架。在这篇文章中,新的信息熵被提出来,这种信息熵能够将其它特殊关系的不确定度量方法统一在一个理论框架中。1.一般模糊二元关系的信息熵首先引入了一个新的熵去度量模糊二元关系的信息量并且给出了联合熵,条件熵与互信息,讨论了这些不确定性度量的性质。然后将这种熵运用到信息表与决策表中来刻画基于熵的属性约简定义。最后,提出了一般模糊二元关系的另一种不确定性度量—模糊邻域熵与它的派生熵,并讨论了两种熵的等价性。一般模糊二元关系的信息熵是特殊关系熵的推广,不仅能够处理单一结构关系(等价关系、相似关系、优势关系)的不确定信息,而且能够度量异构关系的不确定性,在数据处理及信息挖掘领域具有潜在应用。2.一般模糊二元关系的广义信息熵一般模糊二元关系的模糊信息熵忽略了模糊邻域的部分信息,只考虑其局部信息。为此,本文定义一般模糊关系的广义模糊信息熵的概念,该熵是Shannon熵的另一种推广形式。同时,给出了广义模糊联合熵,广义条件熵和互信息的概念,讨论了这些不确定性度量的关系及其重要性质,并讨论了广义模糊熵与一般模糊关系熵的区别与联系。最后,将所提出的广义模糊熵运用到信息表与决策表中来刻画属性约简的定义。较一般模糊二元关系的信息熵相比,广义模糊信息熵考虑了模糊关系的更多信息。
[Abstract]:Relationship is an important concept to describe the interrelation between elements. It is widely used in the field of academic intelligence, such as relational database, clustering analysis, approximate reasoning, attribute reduction. Classification and decision making. In recent years, some uncertainty measures of special relationships are represented by information entropy. However, so far, there is no systematic method to construct these uncertainty measures into a theoretical framework. New information entropy is proposed, This information entropy can unify the uncertain measures of other special relationships in a theoretical framework. Firstly, a new entropy is introduced to measure the information content of fuzzy binary relations and the joint entropy is given. The properties of these uncertainty measures are discussed. Then the entropy is applied to the information table and decision table to describe the definition of attribute reduction based on entropy. In this paper, another uncertainty measure of the general fuzzy binary relation, fuzzy neighborhood entropy and its derived entropy, is proposed, and the equivalence of the two kinds of entropy is discussed. The information entropy of the general fuzzy binary relation is a generalization of the special relation entropy. It can not only deal with uncertain information of a single structural relationship (equivalence relation, similarity relation, advantage relationship), but also measure the uncertainty of heterogeneous relationship. There are potential applications in data processing and information mining. The generalized information entropy of general fuzzy binary relation and fuzzy information entropy of general fuzzy binary relation ignore some information of fuzzy neighborhood and only consider local information. In this paper, the concept of generalized fuzzy information entropy of general fuzzy relation is defined, which is another extension of Shannon entropy. At the same time, the concepts of generalized fuzzy joint entropy, generalized conditional entropy and mutual information are given. The relations and important properties of these uncertainty measures are discussed, and the difference and relation between generalized fuzzy entropy and general fuzzy relation entropy are discussed. The proposed generalized fuzzy entropy is applied to the information table and decision table to describe the definition of attribute reduction. Compared with the information entropy of the general fuzzy binary relation, the generalized fuzzy information entropy considers more information of the fuzzy relation.
【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】：O159

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