对象集变化时近似集动态维护的矩阵方法

目前粗糙集模型中概念的上、下近似集的计算方法大多是基于静态信息系统的.而实际的信息系统是随时间动态变化的，通常包括对象集、属性集和属性值3种类型的粒度变化，这些变化必然引起概念近似集的动态变化.如何快速、有效地更新概念的近似集是基于粗糙集的动态知识更新中的热点研究问题之一.而利用既有知识的增量式更新方法是一种有效的近似集动态更新方法.在信息系统动态变化的客观环境下，以矩阵作为表达和运算工具从一个全新的视角研究信息系统的论域随时间变化时，变精度粗糙集模型中概念的上、下近似集的增量式更新方法，并构造出近似集增量式更新的矩阵算法，随后分析了算法的时间复杂度。进一步，在MATLAB平台上开发出增量式更新和非增量式更新近似集的两种矩阵算法的程序，最后在UCI的6个数据集上测试了两种矩阵算法的性能并将实验结果进行比较，结果表明增量式更新的矩阵算法可行、简洁和高效.

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.