Abstract: Positive region is one of the core concepts in rough set theory, and the algorithm complexity for computing positive region affects implementations of the related algorithms directly. With one equivalent definition of positive region, a method for computing positive region is proposed based on diagonal matrix. In this method, every searched compatible object set is stored in the diagonal line of the diagonal matrix and the searched objects are reset to zero so as to reduce the amount of calculation. The example shows that the proposed method has advantages of conveniency for computation, simplicity and intuition, it can improve the efficiency for computation of positive region.

Key words: rough set, positive region, diagonal matrix

摘要： 正区域是粗糙集理论中的核心概念之一，计算正区域的算法复杂度直接影响到其他算法的实现。借助于正区域的一种等价定义，提出了一种基于对角矩阵的计算正区域的方法。该方法把每次搜索到的相容对象集存放在对角矩阵的对角线上，并把已经搜索的对象进行归零处理，从而减少计算量。实例表明该方法计算方便，简单直观，能提高计算正区域的效率。

关键词: 粗糙集, 正区域, 对角矩阵