Structural features of attribute reduction matrix and layer fast algorithm

Current algorithms provide only feasible attribute reductions,they are not necessarily the minimum ones. Thus,it is significant to analyze the characteristics of attribute reduction and get the minimum one from all reductions. Firstly,an attribute reduction matrix is defined based on the information system.The attribute reduction can be characterized by the structural features of the matrix.Then,a layer fast algorithm by matrix algebraic theory is proposed to solve the problem.Finally,numerical results are given to show the advantage of our method by highly reducing the computational cost.