Attribute reduction in object oriented concept lattices based on congruence relations

Abstract

This paper studies a new definition and an approach to attribute reduction in an object oriented concept lattice based on congruence relations. Firstly, dependence space based on the object oriented concept lattice is researched to obtain the relationship among object oriented concept lattices and the corresponding congruence relations. Then the notion of attribute reduct in this paper, resembling that in rough set theory, is defined to find minimal attribute subsets which can preserve all congruence classes determined by the attribute set. Finally, an approach of discernibility matrix is presented to calculate all attribute reducts. It is shown that attribute reducts can also keep all object oriented extents and their original hierarchy in the object oriented concept lattice.