Attribute reduction in concept lattices based on deletion transformations

This paper constructs deletion transformations based on concept lattices. It is proved that the deletion transformation is surjective from the concept lattice of a context to that of its sub-context. Using deletion transformations, the concept lattice of any subcontext can be derived from the original concept lattice directly. As an application, attribute reduction in concept lattices are reconsidered from the viewpoint of deletion transformations. Moreover, definition of attribute reduction in concept lattices is developed, and judgment of attribute reducts is also provided based on deletion transformations.