Attribute Reduction And Rough Approximations In Concept Lattices

The paper presents approaches to attribute reduction and rough approximations in formal concept lattices. After discussing the basic units of extent sets and intent sets in a formal context, we define a concept of covering reduct of extents. It is proved that a covering consistent set of extents and a granule consistent set are equivalent. Furthermore, an attribute consistent set of concept lattice must be a covering consistent set of extents (a granule consistent set). A novel method of attribute reduction in formal context lattices is proposed by employing the discernibility attribute set of the basic units of extents. Finally, we introduce some new concepts of upper and lower approximations based on the basic units of extents and intents. The basic properties of these concepts are discussed, and the relationships among some existed concepts of rough approximations are also studied.