对偶概念格的属性约简

Attribute Reduction in Dual Concept Lattices

概念格理论是研究概念和概念之间层次结构的一种强有力的工具。概念格是根据数据之间的关系建立起来的,已经被应用于数据挖掘、软件工程、信息检索和粗糙集等领域。属性约简是概念格理论研究的核心问题之一。通过探讨对偶概念格与Wille教授提出的概念格之间的联系,得出对偶概念格与概念格的协调集是相同的。结合概念格协调集的判定定理得出了对偶概念格协调集的判定定理,并利用对偶概念格与概念格的对偶性,在概念格属性约简的基础上给出了对偶概念格属性约简的方法。

The theory of concept lattice is a powerful tool for the study of formal concepts and conceptual hierarchies. Concept lattice is constructed from a relational database, and is used in many application fields, such as data mining, software engineering, information retrieval and rough set, etc. Attribute reduction is one of the key problems in the study of concept lattices. This paper studies attribute reduction in dual concept lattices. By exploring the relationship between the dual concept lattice and Wille＇s lattice, it is proved that the consistent sets in the two lattices are the same. On the basis of the theorem of consistent sets in Wille＇s lattice, this paper obtains the theorem of consistent sets in dual concept lattices. Based on the duality of the two concept lattices and the methods of attribute reduction in Wille＇s lattice, this paper proposes an approach to attribute reduction in dual concept lattices.