理论数学

Vol.6 No.5 (September 2016)

概念格与拓扑
Concept Lattice and Topology

 

作者:

李伯权 :安徽师范大学数学计算机科学学院,安徽 芜湖

鲍玉曦 :南京师范大学附属中学树人学校,江苏 南京

 

关键词:

形式背景概念格属性约简可辨识属性矩阵子基约简Formal Context Concept Lattice Attribute Reduction Distinguishable Attributes Matrix Subbase Reduction

 

摘要:

概念格是根据形式背景中信息建立起来的数据结构,这一结构从本质上揭示了对象与属性之间的关系。它是数据中概念发现的有效工具,广泛应用在情报检索、数字式图书馆、软件工程和知识发现领域。概念格中的属性约简是其研究的一个重要内容。鉴于形式背景与点集拓扑这两者在研究方法上有许多相似之处,本文尝试从拓扑学角度来观看概念格中的属性约简,建立其与拓扑学中子基约简的某种联系。接着由拓扑子空间的构造方法来定义形式背景上的限制及叉乘,看是否能保持一些拓扑性质的不变,从而丰富了形式背景的研究内容。

The concept lattice is the structure of dates which is established according to the information in formal context. This structure reveals the nature of the relationship between attributes of the object. It is an effective tool for concept discovery from dates and has been widely used in information retrieval, digital library, software engineering and knowledge discovery. The attribute reduction is important. There are a lot of similarities in the research technique between formal context and topology. This paper tries to watch attribute reduction in concept lattice from the perspective of topology, establishing some connections with subbase reduction in topology. This paper tries to define the restrictions and product of formal context according to the definition of a new topological space, looking whether some topological property can be maintained. Thus the content of formal context has been enriched in some degree.

文章引用:

李伯权 , 鲍玉曦 (2016) 概念格与拓扑。 理论数学, 6, 427-436. doi: 10.12677/PM.2016.65058

 

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