Some Separations in Covering Approximation Spaces
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32795
Some Separations in Covering Approximation Spaces

Authors: Xun Ge, Jinjin Li, Ying Ge


Adopting Zakowski-s upper approximation operator C and lower approximation operator C, this paper investigates granularity-wise separations in covering approximation spaces. Some characterizations of granularity-wise separations are obtained by means of Pawlak rough sets and some relations among granularitywise separations are established, which makes it possible to research covering approximation spaces by logical methods and mathematical methods in computer science. Results of this paper give further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.

Keywords: Rough set, covering approximation space, granularitywise separation.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1626


[1] Z. Bonikowski, E. Bryniarski and U. Wybraniec, Extensions and intentions in the rough set theory, Information Sciences, 107(1998), 149-167.
[2] R. Engelking, General Topology, revised and completed edition, Heldermann, Berlin: 1989.
[3] Y. Ge, Granularity-wise separations in covering approximation spaces, 2008 IEEE International Conference on Granular Computing, 238-243.
[4] A. Jackson, Z. Pawlak and S. LeClair, Rough sets applied to the discovery of materials knowledge, Journal of Alloys and Compounds, 279(1998), 14-21.
[5] M. Kryszkiewicz, Rough set approach to incomplete information systems, Information Sciences, 112(1998), 39-49.
[6] E. Lashin, A. Kozae, A. Khadra and T. Medhat, Rough set theory for topological spaces, International Journal of Approximate Reasoning, 40(1-2)(2005), 35-43.
[7] Y. Leung, W. Wu and W. Zhang, Knowledge acquisition in incomplete information systems: A rough set approach, European Journal of Operational Research, 168(2006), 164-180.
[8] Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11(1982), 341-356.
[9] Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning About Data, Kluwer Academic Publishers, Boston: 1991.
[10] J. A. Pomykala, Approximation operations in approximation space, Bull. Pol. Acad. Sci., 9-10(1987), 653-662.
[11] K. Qin, Y. Gao and Z. Pei, On covering rough sets, Lecture Notes in Artificial Intelligence, 4481(2007), 34-41.
[12] E. C. C. Tsang, D. Chen and D. S. Yeung, Approximations and reducts with covering generalized rough sets, Computers and Mathematics with Applications, 56(2008), 279-289.
[13] Y. Yao, Views of the theory of rough sets in finite universes, International Journal of Approximate Reasoning, 15(1996), 291-317.
[14] Y. Yao, Relational interpretations of neighborhood operators and rough set approximation operators, Information Sciences, 111(1998), 239-259.
[15] Y. Yao, On generalizing rough set theory, Lecture Notes in Artificial Intelligence, 2639(2003), 44-51.
[16] Y. Yao, Three-Way Decision: An Interpretation of Rules in Rough Set Theory, Lecture Notes in Computer Science, 5589(2009), 642-649.
[17] W. Zhu, Topological approaches to covering rough sets, Information Sciences, 177(2007), 1499-1508.
[18] W. Zhu, Relationship between generalized rough sets based on binary relation and covering, Information Sciences, 179(2009), 210-225.
[19] W. Zhu and F. Wang, Covering Based Granular Computing for Conflict Analysis, Lecture Notes in Computer Science, 3975(2006), 566-571.
[20] W. Zhu and F. Wang, On Three Types of Covering Rough Sets, IEEE Transactions on Knowledge and Data Engineering, 19(8)(2007), 1131- 1144.