Lattice description of approximation space

Knowledge reduction is one of the main problems in rough sets theory. The attribute reduction algorithms of decision table based on discernible matrix are required to construct discernible matrix, which is the core of the algorithms,the process is associated with the intersection of sets and discernibility function computing, in this paper, the system is equipped with a lattice structure, the operations on the decision table are transmitted into lattice operation, in this frame, we pave a way to explore the attribute reduction with lattice approaches.