Approaches to Attribute Reduction in Concept Lattices Based on Rough Set Theory

This paper mainly proposes notions and methods of attribute reduction in concept lattices based on rough set theory. Using dependence space of concept lattices, we first discuss the relationships between congruence relations and the corresponding concept lattices. We then define notions of attribute reduction in a formal context based on congruence relations which is to find the minimal attribute subsets preserving the congruence partition. Finally, we define discernibility matrices and Boolean functions of a formal context to calculate all attribute reducts and analyze attribute characteristics. Using this notion of attribute reduction, methods, results as well as their proof about attribute reduction in a formal context can be derived directly by those in rough set theory. Furthermore, we prove that the attribute reducts proposed in this paper also preserve all extents of formal concepts and their original hierarchy in the concept lattice.