A Matrix-Based Approach for Maintenance of Approximations under the Variation of Object Set

At present, most methods for calculating upper and lower approximations of a concept are based on the premise that the information system is static. In fact, the information system usually varies with time, including the variations of the universe, the attribute set and the attributes' values. These variations all result in the corresponding change of approximations of a concept in rough sets. How to update the approximations rapidly and efficiently is one of the hot issues on rough sets based dynamic knowledge discovery. The incremental updating method, in which the pre-existing knowledge is fully utilized, is one of the effective methods for updating approximations dynamically. In this paper, a matrix-based incremental method for updating the approximations under variable precision rough sets is presented from a new viewpoint while the universe of information system evolves over time. Then the corresponding algorithms are designed and their computational time complexities are analyzed. Furthermore, the programs corresponding to the algorithms are developed on MATLAB. Finally, the experiments on UCI datasets are designed to evaluate the performance of the proposed matrix-based incremental method and the matrix-based non-incremental method. The comparison of the experimental results demonstrates the feasibility, conciseness and validity of the proposed matrix-based incremental method.