Covering-based Rough sets Based on the Refinement of Covering-element
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.
[1] Z. Pawlak, "Rough sets," International Journal of Computer and Information
Sciences, pp. 341-356, 1982.
[2] 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.
[3] 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.
[4] 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.
[5] M. Kryszkiewicz, "Rough set approach to incomplete information systems,"
Information sciences, vol. 112, pp. 39-49, 1998.
[6] 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.
[7] 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.
[8] 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.
[9] 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.
[1] Z. Pawlak, "Rough sets," International Journal of Computer and Information
Sciences, pp. 341-356, 1982.
[2] 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.
[3] 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.
[4] 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.
[5] M. Kryszkiewicz, "Rough set approach to incomplete information systems,"
Information sciences, vol. 112, pp. 39-49, 1998.
[6] 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.
[7] 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.
[8] 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.
[9] 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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:57754", author = "Jianguo Tang and Kun She and William Zhu", title = "Covering-based Rough sets Based on the Refinement of Covering-element", abstract = "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.", keywords = "Determinate element, indeterminate element, refinementof covering-element, refinement of covering, covering-basedrough sets.", volume = "5", number = "8", pages = "1308-11", }
