Some Separations in Covering Approximation Spaces

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.

Authors:

• Xun Ge
• Jinjin Li
• Ying Ge

Keywords:

• Rough set
• covering approximation space
• granularitywise separation.

References:

[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.