Covering-Based Reduction of Property-Oriented Concept Lattices

A method to reduce the property-oriented concept lattice of a formal context directly is proposed in this paper. The similarity degree between object sets and the similarity degree between attribute sets are firstly introduced, and then, object neighborhood and attribute neighborhood are created accordingly. The sizes of object neighborhood or the attribute neighborhood are adjusted by the similarity degrees, thus, the number of the property-oriented concepts can be controlled and the property-oriented concept lattice is compressed. Using this method, we can compress the property-oriented concept lattice from the viewpoints of object covering and attribute covering, and the most important is that the reduced lattice is a subset of the original one.