Using Covering Reduction to Identify Reducts for Object-Oriented Concept Lattices

Abstract

An object-oriented concept lattice, as an important generalization of classic concept lattices, is a bridge between formal concept analysis and rough set theory. This paper presents an application of covering reduction in formal concept analysis. It studies attribute reduction, object reduction, and bireduction for object-oriented concept lattices. We show that attribute and object reductions for object-oriented concept lattices are equivalent to covering reductions. Using a Boolean matrix transformation, we derive the corresponding algorithms to identify all reducts. In contrast to existing discernibility matrix-based reduction algorithms for object-oriented concept lattices, our algorithms omit the calculation of concept lattices, discernibility matrices, and discernibility functions. The algorithms save substantial time and are a significant improvement over discernibility matrix-based techniques.