Neighborhood is an important concept in covering based rough sets. That under what condition neighborhoods form a partition is a meaningful issue induced by this concept. Many scholars have paid attention to this issue and presented some necessary and sufficient conditions. However, there exists one common trait among these conditions, that is they are established on the basis of all neighborhoods have been obtained. In this paper, we provide a necessary and sufficient condition directly based on the covering itself. First, we investigate the influence of that there are reducible elements in the covering on neighborhoods. Second, we propose the definition of uniform block and obtain a sufficient condition from it. Third, we propose the definitions of repeat degree and excluded number. By means of the two concepts, we obtain a necessary and sufficient condition for neighborhoods to form a partition. In a word, we have gained a deeper and more direct understanding of the essence over that neighborhoods form a partition.
An improved approach to attribute reduction with covering rough sets
Bohai University（渤海大学）；Harbin Institute of Technology（哈尔滨工业大学）
属性约简是模式识别和数据采掘的重要预处理步骤。大多数的研究都集中在属性约简的粗糙集。最近，Tsang等人在文献[E. C.C. Tsang，D.作者：Daniel S. Yeung，Approximations and Reducts with Covering Generalized Rough Sets，Computers and Mathematics with Applications 56（2008）279-289]，其中提出了一种基于可扩展矩阵的方法来计算所有属性约简。本文提出了一种改进的方法，即利用覆盖粗糙集构造更简单的区分矩阵，并对Tsang等人关于属性约简的一些刻画进行了改进，证明了改进后的区分矩阵与原区分矩阵等价，但区分矩阵的计算复杂性大大降低.
DIDLM: A SLAM Dataset for Difficult Scenarios Featuring Infrared, Depth Cameras, LIDAR, 4D Radar, and Others under Adverse Weather, Low Light Conditions, and Rough Roads
School of Information Science and Technology, Northwest University（信息科学与技术学院，西北大学）；Department of Electrical and Computer Engineering, The University of British Columbia（电气与计算机工程系，不列颠哥伦比亚大学）
