Classification and reduction of attributes in concept lattices

We investigate the attribute classification and the reduction of concept lattices within the framework of rough set theory. Based on the binary relation between objects and attributes in a formal context, the properties of the irreducible elements on extent closure systems and the congruence on semi-lattices are discussed. Two kinds of classification methods for attributes by means of the properties are proposed. Using the classification, the reducts of concept lattices can be derived.