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On Three Types of Covering-Based Rough Sets
August 2007 (vol. 19 no. 8)
pp. 1131-1144
| ASCII Text | x | ||
| William Zhu, Fei-Yue Wang, "On Three Types of Covering-Based Rough Sets," IEEE Transactions on Knowledge and Data Engineering, vol. 19, no. 8, pp. 1131-1144, August, 2007. | |||
| BibTex | x | ||
| @article{ 10.1109/TKDE.2007.1044, author = {William Zhu and Fei-Yue Wang}, title = {On Three Types of Covering-Based Rough Sets}, journal ={IEEE Transactions on Knowledge and Data Engineering}, volume = {19}, number = {8}, issn = {1041-4347}, year = {2007}, pages = {1131-1144}, doi = {http://doi.ieeecomputersociety.org/10.1109/TKDE.2007.1044}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Knowledge and Data Engineering TI - On Three Types of Covering-Based Rough Sets IS - 8 SN - 1041-4347 SP1131 EP1144 EPD - 1131-1144 A1 - William Zhu, A1 - Fei-Yue Wang, PY - 2007 KW - Rough sets KW - approximation KW - covering KW - data mining KW - reduct KW - fuzzy sets KW - granular computing KW - computing with words. VL - 19 JA - IEEE Transactions on Knowledge and Data Engineering ER - | |||
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.
Index Terms:
Rough sets, approximation, covering, data mining, reduct, fuzzy sets, granular computing, computing with words.
Citation:
William Zhu, Fei-Yue Wang, "On Three Types of Covering-Based Rough Sets," IEEE Transactions on Knowledge and Data Engineering, vol. 19, no. 8, pp. 1131-1144, Aug. 2007, doi:10.1109/TKDE.2007.1044
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