World Academy of Science, Engineering and Technology
Published August 24, 2011 | Version 8682
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Covering-based Rough sets Based on the Refinement of Covering-element

Description

Covering-based rough sets is an extension of rough sets and it is based on a covering instead of a partition of the universe. Therefore it is more powerful in describing some practical problems than rough sets. However, by extending the rough sets, covering-based rough sets can increase the roughness of each model in recognizing objects. How to obtain better approximations from the models of a covering-based rough sets is an important issue. In this paper, two concepts, determinate elements and indeterminate elements in a universe, are proposed and given precise definitions respectively. This research makes a reasonable refinement of the covering-element from a new viewpoint. And the refinement may generate better approximations of covering-based rough sets models. To prove the theory above, it is applied to eight major coveringbased rough sets models which are adapted from other literature. The result is, in all these models, the lower approximation increases effectively. Correspondingly, in all models, the upper approximation decreases with exceptions of two models in some special situations. Therefore, the roughness of recognizing objects is reduced. This research provides a new approach to the study and application of covering-based rough sets.

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References

  • Z. Pawlak, "Rough sets," International Journal of Computer and Information Sciences, pp. 341-356, 1982.
  • J. G. Bazan, J. F. Peters, and A. Skowron, "Behavioral pattern identification through rough set modelling," in 10th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, vol. 3642 LNAI, Regina, Canada, 2005, pp. 688-697.
  • T. Herawan, M. M. Deris, and J. H. Abawajy, "A rough set approach for selecting clustering attribute," Knowledge-Based Systems, vol. 23, pp. 220-231, 2010.
  • Q. Hu, D. Yu, J. Liu, and C. Wu, "Neighborhood rough set based heterogeneous feature subset selection," Information Sciences, vol. 178, pp. 3577-3594, 2008.
  • M. Kryszkiewicz, "Rough set approach to incomplete information systems," Information sciences, vol. 112, pp. 39-49, 1998.
  • D. Parmar, T. Wu, and J. Blackhurst, "Mmr: An algorithm for clustering categorical data using rough set theory," Data and Knowledge Engineering, vol. 63, pp. 877-891, 2007.
  • G.-Y. Wang, Z. Zheng, and Y. Zhang, "Ridas - a rough set based intelligent data analysis system," in Proceedings of 2002 International Conference on Machine Learning and Cybernetics, vol. 2, Beijing, China, 2002, pp. 646-649.
  • X.-Z. Wang, J.-H. Zhai, and S.-X. Lu, "Induction of multiple fuzzy decision trees based on rough set technique," Information Sciences, vol. 178, pp. 3188-3202, 2008.
  • Y. Yao, Y. Zhao, J. Wang, and S. Han, "A model of machine learning based on user preference of attributes," in 5th International Conference on Rough Sets and Current Trends in Computing, vol. 4259 LNAI, Kobe, Japan, 2006, pp. 587-596. [10] W. Zhu and F.-Y. Wang, "Covering based granular computing for conflict analysis," in IEEE International Conference on Intelligence and Security Informatics, vol. 3975 LNCS, San Diego, CA, United states, 2006, pp. 566-571. [11] S. Marcus, "Tolerance rough sets, cech topologies, learning processes," pp. 471-487, 1994. [12] L. Polkowski, A. Skowron, and J. Zytkow, "Tolerance based rough sets," in Soft Computing: Rough Sets, Fuzzy Logic, Neural Networks, Uncertainty Management, San Diego, 1995, pp. 55-58. [13] R. Slowinski and D. Vanderpooten, "A generalized definition of rough approximations based on similarity," Knowledge and Data Engineering, IEEE Transactions on, vol. 12, pp. 331-336, 2000. [14] Y. Y. Yao and S. K. M. Wong, "Generalization of rough sets using relationships between attribute values," pp. 30-33, 1995. [15] Z. Bonikowski, E. Bryniarski, and U. Wybraniec-Skardowska, "Extensions and intensions in the rough set theory," Information sciences, vol. 107, pp. 149-167, 1998. [16] W. Zakowski, "Approximations in the space(u,)," Demonstratio Mathematica, pp. 761-769, 1983. [17] X. Ge and Z. Li, "Definable subsets in covering approximation spaces," International Journal of Computational and Mathematical Sciences, vol. 5, 2010. [18] J. Liu and Z. Liao, "The sixth type of covering-based rough sets," in 2008 IEEE International Conference on Granular Computing, GRC 2008, Hangzhou, China, 2008, pp. 438-441. [19] J. A. Pomykala, "Approximation operations in approximation," Bull.Pol.Acad.Sci., vol. 35, no. 9-10, pp. 653-662, 1987. [20] E. C. C. Tsang, C. Degang, J. W. T. Lee, and D. S. Yeung, "On the upper approximations of covering generalized rough sets," in Proceedings of 2004 International Conference on Machine Learning and Cybernetics, vol. 7, 2004, pp. 4200- 4203. [21] J. Wang, D. Dai, and Z. Zhou, "Fuzzy covering generalized rough sets," Zhoukou Teachers Colloge, vol. 21, pp. 20-22, 2004. [22] M. Wu, X. Wu, T. Shen, and C. Cao, "A new type of covering approximation operators," in 2009 International Conference on Electronic Computer Technology, ICECT 2009, Macau, China, 2009, pp. 334-338. [23] Z. Xu and Q. Wang, "On the properties of covering rough sets model," Henan Normal University.(Nat.Sci), vol. 33, no. 1, pp. 130-132, 2005. [24] Y. Y. Yao, "On generalizing pawlak approximation operators," in Proceedings of the First International Conference, RSCTC98, vol. 1424, 1998, pp. 298-298. [25] W. Zhu, "Relationship between generalized rough sets based on binary relation and covering," Information Sciences, vol. 179, pp. 210-225, 2009. [26] ÔÇöÔÇö, "Topological approaches to covering rough sets," Information Sciences, vol. 177, pp. 1499-1508, 2007. [27] W. Zhu and F. Wang, "A new type of covering rough set," in 2006 3rd International IEEE Conference on Intelligent Systems, IS-06, London, United kingdom, 2006, pp. 444-449. [28] ÔÇöÔÇö, "Reduction and axiomization of covering generalized rough sets," Information Sciences, vol. 152, pp. 217-230, 2003. [29] Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning about Data. Boston: Kluwer Academic Publishers, 1991. [30] D. Miao and D. Li, Rough Sets Theory , Algorithms and Applications. Tsinghua university press, 2008. [31] W. Qiu and Z. Luo, "Research on generalized rough sets based on fine covering," Journal of Guangdong University of Technology, vol. 04, pp. 93-97, 2006. [32] F. Zhu, "On covering generalized rough sets," Master-s thesis, The University of Arizona, 2002. [33] W. Zhu, "Some results on covering generalized rough sets," Pattern recognition and artificial intelligence, vol. 15, pp. 6-13, 2002. [34] W. Zhu and F. Wang, "On three types of covering-based rough sets," IEEE Transactions on Knowledge and Data Engineering, vol. 19, pp. 1131-1143, 2007. [35] ÔÇöÔÇö, "Relationships among three types of covering rough sets," in 2006 IEEE International Conference on Granular Computing, Atlanta, GA, United states, 2006, pp. 43-48.