Algorithm for decision rules reduction in incomplete information system based on binary discernibility matrix

Being an important topic of the knowledge reduction of rough set, the reduction of the decision rules respectively eliminates the redundant attribute values of each decision rule based on rough logic. The definition of the binary discernibility matrix in the incomplete decision system was given by analyzing all kinds of definitions of the binary discernibility matrix. An algorithm for decision rules reduction in incomplete information system was designed based on binary discernibility matrix. This algorithm is suitable for both compatible and incompatible decision table. The correctness of the proposed algorithm was proved by examples and the efficiency was indicated by empirical analysis and applications.