Topological Properties for Approximation Operators in Covering Based Rough Sets
We investigate properties of approximation operators being closure and topological closure in a framework of sixteen pairs of dual approximation operators, for the study of covering based rough sets. We extended previous results about approximation operators related with closure operators.
KeywordsCovering rough sets Approximation operators Topological closure
- 13.Tsang, E., Chen, D., Lee J., Yeung, D.S.: On the upper approximations of covering generalized rough sets. In: Proceedings of the 3rd International Conference on Machine Learning and Cybernetics, pp. 4200–4203 (2004)Google Scholar
- 23.Zhaowen, L.: Topological structure of generalized rough sets. IEEE Trans. Knowl. Data Eng. 19(8), 1131–1144 (2012)Google Scholar
- 24.Zhu, W.: Properties of the first type of covering-based rough sets. In: Proceedings of Sixth IEEE International Conference on Data Mining - Workshops, pp. 407–411 (2006)Google Scholar
- 25.Zhu, W.: Properties of the second type of covering-based rough sets. In: Proceedings of the IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology, pp. 494–497 (2006)Google Scholar
- 26.Zhu, W.: Basic concepts in covering-based rough sets. In: Proceedings of Third International Conference on Natural Computation, pp. 283–286 (2007)Google Scholar
- 27.Zhu, W.: Properties of the third type of covering-based rough sets. In: Proceedings of International Conference on Machine Learning and Cybernetics, pp. 3746–2751 (2007)Google Scholar
- 30.Zhu, W., Wang, F.: A new type of covering rough set. In: Proceedings of Third International IEEE Conference on Intelligence Systems, pp. 444–449 (2006)Google Scholar
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