Issue No. 08 - August (2007 vol. 19)
Rough set theory is a useful tool for data mining. It is based on equivalence relations and has been extended to covering-based generalized rough set. This paper studies three kinds of covering generalized rough sets for dealing with the vagueness and granularity in information systems. First, we examine the properties of approximation operations generated by a covering in comparison with those of the Pawlak's rough sets. Then, we propose concepts and conditions for two coverings to generate an identical lower approximation operation and an identical upper approximation operation. After the discussion on the interdependency of covering lower and upper approximation operations, we address the axiomization issue of covering lower and upper approximation operations. In addition, we study the relationships between the covering lower approximation and the interior operator and also the relationships between the covering upper approximation and the closure operator. Finally, this paper explores the relationships among these three types of covering rough sets.
data mining, fuzzy set theory, rough set theory,rough set theory, data mining, covering generalized rough sets, information systems,Rough sets, Set theory, Data mining, Information systems, Fuzzy set theory, Fuzzy sets, Internet, Humans, Data analysis, Fuzzy logic,Rough sets, approximation, covering, data mining, reduct, fuzzy sets, granular computing, computing with words.
"On Three Types of Covering-Based Rough Sets", IEEE Transactions on Knowledge & Data Engineering, vol. 19, no. , pp. 1131-1144, August 2007, doi:10.1109/TKDE.2007.1044