Attribute Reduction in Dual Concept Lattices

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 Willee?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 Willee?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 Willee?s lattice, this paper proposes an approach to attribute reduction in dual concept lattices.