关键词: 形式概念, 对偶概念格, 属性约简, 协调集, 约简集

Abstract: 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.

Key words: formal concept, dual concept lattice, attribute reduction, consistent set, reduction set