Concept Lattice and Topology
Abstract: 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
 Wille, R. (1982) Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts. In: Ivan Rival, R., Ed., Ordered Sets, Reidel, Dordecht, Boston, 445-470. http://dx.doi.org/10.1007/978-94-009-7798-3_15
 Ganter, B. and Wille, R. (1999) Formal Concept Analysis: Mathematical Foundations. Springer, Berlin. http://dx.doi.org/10.1007/978-3-642-59830-2
 张文修, 魏玲, 祁建军. 概念格的属性约简理论与方法[J]. 中国科学(E辑 信息科学), 2005, 35(6): 628-639.
 熊金城. 点集拓扑讲义[M]. 北京: 高等教育出版社, 1998: 38-105.
 Kelley, J.L., 著. 一般拓扑学[M]. 吴让泉, 译. 北京: 科学出版社, 1982: 91-216.
 余玄冰. 点集拓扑[M]. 北京: 北京师范大学出版社, 1983: 25-65.
 吴东兴. 点集拓扑学基础[M]. 北京: 科学出版社, 1982: 20-120.