覆盖粗集的覆盖约简及拓扑式研究

发布时间：2018-01-05 21:08

  本文关键词：覆盖粗集的覆盖约简及拓扑式研究　出处：《扬州大学》2017年硕士论文　论文类型：学位论文

  更多相关文章： 覆盖粗集 广义近似空间 拓扑 粗糙连续 分离性 紧性 覆盖(饱和)约简 诱导拓扑 诱导粗集

【摘要】：波兰数学家Pawlak于1982年提出了处理不确定性问题的粗糙集理论,它作为一种数据分析处理理论,已成为信息科学最为活跃的研究领域之一,并被成功地应用于医药科学、材料科学、管理科学等领域.广义近似空间(又称关系粗集)及覆盖近似空间(又称覆盖粗集)是对Pawlak经典粗集模型的重要推广.对覆盖粗集类似拓扑空间中的性质及其约简的探究是研究覆盖粗集的重要内容.本文利用覆盖粗集的覆盖作为子基诱导了一个拓扑空间,定义了覆盖粗集的多种分离性、紧性等概念,并研究了它们的性质及相互关系.此外对关系粗集利用其诱导覆盖粗集定义了 s-紧,p-紧和双紧等紧性,并研究了它们的关系及在粗糙连续映射下的保持性.本文还研究了覆盖粗集的覆盖约简与覆盖饱和约简,证明了当U有限时覆盖约简是存在的,而覆盖饱和约简不仅存在而且唯一并给出了可行的算法求解覆盖饱和约简.本文共分为五章.第一章是引言与预备,简单介绍粗糙集理论的发展概况及本文写作背景,同时给出了若干预备知识.第二章引入诱导关系粗集和诱导覆盖粗集,给出了几种覆盖粗集诱导关系粗集及关系粗集诱导覆盖粗集的方式.第三章借助覆盖粗集所诱导的拓扑空间的拓扑定义了覆盖粗集的分离性并给出了它们的刻画.借助诱导覆盖粗集的紧性,定义了广义近似空间的s-紧,p-紧和双紧,并研究了这三种紧性与关系紧、拓扑紧之间的关系.同时讨论了上述五种紧性在粗糙连续映射下的保持性.第四章对于覆盖粗集引入了覆盖约简,覆盖饱和约简的概念和覆盖的核的概念,研究了覆盖约简和覆盖饱和约简的相关性质.证明了当论域有限时覆盖约简的存在性及覆盖饱和约简的存在唯一性.说明了覆盖约简不必是覆盖饱和约简,覆盖饱和约简也不必是覆盖约简,并给出覆盖约简成为覆盖饱和约简的特定条件.第五章总结了本文的主要工作以及接下来需要进一步探究的课题.
[Abstract]:Poland mathematician Pawlak proposed to deal with the uncertainty problem of rough set theory in 1982, it is a kind of data analysis theory, has become one of the most active research in the field of information science, and has been successfully applied in medical science, materials science, management science and other fields. Generalized approximate space (called rough set) and the covering approximation space (also called covering rough set) is an important extension to Pawlak classic rough set model. To explore the nature and the reduction of covering rough set is similar in topological spaces is an important research content of covering rough set. This paper use the covering rough set covering as a sub base induces a topological space, the definition of a variety of separation covering rough sets, the concept of compactness, and studied their properties and relations. In addition to the induction of covering rough set s- is defined by the tight relationship between rough sets, p- and double tight tight tight, and research Their relationship and in the rough continuous mapping of retention. This paper also studies the coverage reduction of covering rough set and saturation coverage reduction, it is proved that when U limited coverage reduction exists, and the existence and uniqueness of saturation coverage reduction algorithm and gives the feasible coverage saturation reduction. This article is divided into the five chapter. The first chapter is the introduction and preparation, introduces the development of rough set theory survey and the background of this writing, and gives some preliminary knowledge. The second chapter introduced the induced relations between rough sets and rough sets are given guidance coverage, several covering rough set relationship induced by rough set and rough set relationship by covering rough set approach. The third chapter with topological topological space covering rough set by definition is given and the separation of covering rough set are depicted. The compactness induced covering rough set, the definition of the generalized approximate space s- Tight, tight and p- double tight, and study the three kinds of compactness and tight relationship, relationship between compact topology. At the same time keep in rough continuous mapping. The five kinds of compactness are discussed. The fourth chapter for covering rough set is introduced covering reduction, the concept of coverage reduction and coverage of the saturated nucleus the concept, properties and saturation coverage coverage reduction reduction. We prove the existence and uniqueness of saturation coverage reduction when the domain of finite covering reduction. The coverage reduction does not need to be covered with saturation coverage reduction, reduction need not be saturated covering reduction, and the reduction of a certain condition coverage saturation reduction. The fifth chapter summarizes the main work of this paper, then the need to further explore the topic.

【学位授予单位】：扬州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP18
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本文编号：1384828