Attribute reduction is a difficult topic in rough set theory and knowledge granularity reduction is one of the important types of reduction. However, up to now, its reduction algorithm based on a discernibility matrix has not been given. In this paper, we show that knowledge granularity reduction is equivalent to both positive region reduction and X-absolute reduction, and derive its corresponding algorithm based on a discernibility matrix to fill the gap. Particularly, knowledge granularity reduction is the usual positive region reduction for consistent decision tables. Finally, we provide a simple knowledge granularity reduction algorithm for finding a reduct with the help of binary integer programming, and consider six UCI datasets to illustrate our algorithms.

属性约简是粗糙集理论中的一个难题，知识粒度约简是约简的重要类型之一。但是，到目前为止，还没有给出基于可分辨矩阵的约简算法。在本文中，我们表明知识粒度的减少等同于正区域减少和X绝对减少，并基于可分辨矩阵来推导其相应算法以填补空白。特别是，知识粒度的减少是一致决策表通常的积极区域减少。最后，我们提供了一种简单的知识粒度减少算法，以借助二进制整数编程来找到约简，并考虑了六个UCI数据集来说明我们的算法。