Object-oriented interval-set concept lattices

Abstract

Formal concept analysis and rough set are two kinds of efficient mathematical tools for data analysis and knowledge discovery. By combining these two theories, object-oriented and property-oriented concept lattices are proposed. Interval set theory is proposed to describe a partially-known concept by a lower bound and a upper bound. In order to obtain the more accurate extension and intension for a partially-known object-oriented concept, we introduce the theory of interval sets into the object-oriented concept lattice, and propose an object-oriented interval-set concept lattice. Properties of them are investigated. Relationships among interval-set concept lattices, object-oriented interval-set concept lattices and property-oriented interval-set concept lattices are discussed. By discussing the relationships between the object-oriented concept lattice and the object-oriented interval-set concept lattice, an approach to construct object-oriented interval-set concept lattices are established.