2012/09/29 by Aiping Huang, Huang, Aiping, William Zhu +1
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Image Processing and 3D Reconstruction #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.1210.0074
openalex publication_date 2012/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Covering-based rough set theory is a useful tool to deal with inexact, uncertain or vague knowledge in information systems. Topology, one of the most important subjects in mathematics, provides mathematical tools and interesting topics in studying information systems and rough sets. In this paper, we present the topological characterizations to three types of covering approximation operators. First, we study the properties of topology induced by the sixth type of covering lower approximation operator. Second, some topological characterizations to the covering lower approximation operator to be an interior operator are established. We find that the topologies induced by this operator and by the sixth type of covering lower approximation operator are the same. Third, we study the conditions which make the first type of covering upper approximation operator be a closure operator, and find that the topology induced by the operator is the same as the topology induced by the fifth type of covering upper approximation operator. Forth, the conditions of the second type of covering upper approximation operator to be a closure operator and the properties of topology induced by it are established. Finally, these three topologies space are compared. In a word, topology provides a useful method to study the covering-based rough sets.