摘要： 为解决非对称容差关系存在冗余容差类问题以及为提高近似集的计算效率。本文通过改进的非对称容差关系，介绍了不完备信息系统中上、下近似集的布尔矩阵表示方法，设计了计算近似集的矩阵分块算法，并在GPU上实现近似集计算过程的加速。具体来说，本文提出了一种最近容差关系，构建了不完备信息系统中对象之间的层次结构，这些结构被转换成多个局部关系矩阵，以此来快速计算最近容差类。最后，向量化的最近容差类被分批加载到显存来计算近似集。UCI数据集和用户自定义数据集上的实验结果表明，在基于最近容差关系上，减少了容差类，矩阵分块算法在GPU上实现了对近似集计算过程的有效加速，相比于CPU计算和分布式计算，GPU分块算法执行速度平均分别提高了16.69倍和3.89倍。

Abstract: To address the problem of redundant tolerance classes in asymmetric tolerance relation, and to improve the computational efficiency of approximations. this paper introduces a Boolean matrix representation of the upper and lower approximations based on improved tolerance relation, and designs a block-matrix algorithm, and accelerates the approximations calculation process on GPU. Specifically, this paper proposes a nearest tolerance relation to construct the structure between objects in incomplete information systems, these structures are transformed into multiple local relation matrices to quickly calculate the nearest tolerance class, these vectorized class are loaded in blocks into memory to calculate the approximations. The experimental results on the UCI dataset and user-defined dataset show that the tolerance class has been reduced, the block-matrix algorithm based on the nearest tolerance relation effectively accelerates the approximates computation process on GPU, compared with CPU and distributed computing, the average execution speed of block-matrix algorithm has increased by 16.69 times and 3.89 times respectively.