• 热点与综述 •

### 基于矩阵的粗糙集近似集快速计算算法

1. 1. 安徽大学 计算智能与信号处理教育部重点实验室, 合肥 230039;
2. 安徽大学 计算机科学与技术学院, 合肥 230601;
3. 安徽大学 物质科学与信息技术研究院, 合肥 230031
• 收稿日期:2022-04-28 修回日期:2022-06-13 发布日期:2022-08-19
• 作者简介:徐怡(1981-),女,教授、博士,CCF会员,主研方向为智能信息处理、粒计算、边缘计算;侯迪,硕士研究生。
• 基金资助:
安徽省自然科学基金 （2008085MF194，1308085QF114，1908085MF188）；安徽省高等学校省级自然科学基金项目（KJ2013A015）。

### Fast Calculation Algorithm of Approximations in Rough Sets Based on Matrices

XU Yi1,2, HOU Di3

1. 1. Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei 230039, China;
2. School of Computer Science and Technology, Anhui University, Hefei 230601, China;
3. Institute of Physical Science and Information Technology, Anhui University, Hefei 230031, China
• Received:2022-04-28 Revised:2022-06-13 Published:2022-08-19

Abstract: The calculation of upper and lower approximations is the core issue in rough set theory. Matrices can provide an efficient method for calculating the upper and lower approximations of concepts in rough set models. However，in current matrix methods，each object in the universe must be operated on with all objects in the universe， resulting in a significant time cost.To improve the efficiency of calculating approximations using matrices，a matrix method is proposed for quickly calculating upper and lower approximations. For a given concept，a local relational matrix is constructed based on the extensions of the concept and its complement. Matrix operations are performed on the local relational and identity matrices to obtain positive and boundary domain Boolean matrices. Subsequently，matrix operations are performed on the transposition of the local relational and identity matrices to obtain negative and boundary domain Boolean matrices. In this matrix method，only calculating the approximation based on the local relational matrix is necessary，that is，each object in the universe can be divided into corresponding regions without needing to perform operations on all objects in the universe，which significantly reduces the number of operations of the algorithm compared with traditional matrix algorithms，thereby reducing the time cost. Experiments on eight open datasets show that，compared with four traditional matrix algorithms，the proposed matrix algorithm can improve the running speed by at least 70% and effectively improve the efficiency of the approximation calculation.