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On axiomatic characterizations of three pairs of covering based approximation operators |
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| Authors: | Yan-Lan Zhang Jinjin Li |
| Affiliation: | a College of Mathematics, Sichuan University, Cheng’du, Si’chuan 610064, PR China b Department of Mathematics, Zhangzhou Normal University, Zhang’zhou, Fu’jian 363000, PR China c School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang 316004, PR China d Department of Computer Sciences and Engineering, Zhangzhou Normal University, Zhang’zhou, Fu’jian 363000, PR China |
| Abstract: | Rough set theory is a useful tool for dealing with inexact, uncertain or vague knowledge in information systems. The classical rough set theory is based on equivalence relations and has been extended to covering based generalized rough set theory. This paper investigates three types of covering generalized rough sets within an axiomatic approach. Concepts and basic properties of each type of covering based approximation operators are first reviewed. Axiomatic systems of the covering based approximation operators are then established. The independence of axiom set for characterizing each type of covering based approximation operators is also examined. As a result, two open problems about axiomatic characterizations of covering based approximation operators proposed by Zhu and Wang in (IEEE Transactions on Knowledge and Data Engineering 19(8) (2007) 1131-1144, Proceedings of the Third IEEE International Conference on Intelligent Systems, 2006, pp. 444-449) are solved. |
| Keywords: | Axioms Covering based approximation operators Covering generalized rough sets Rough sets |
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