Definable Subsets in Covering Approximation Spaces

Authors: Xun Ge, Zhaowen Li

Abstract:

Covering approximation spaces is a class of important generalization of approximation spaces. For a subset X of a covering approximation space (U, C), is X definable or rough? The answer of this question is uncertain, which depends on covering approximation operators endowed on (U, C). Note that there are many various covering approximation operators, which can be endowed on covering approximation spaces. This paper investigates covering approximation spaces endowed ten covering approximation operators respectively, and establishes some relations among definable subsets, inner definable subsets and outer definable subsets in covering approximation spaces, which deepens some results on definable subsets in approximation spaces.

Keywords: Covering approximation space, covering approximation operator, definable subset, inner definable subset, outer definable subset.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334552

References:

[1] Z. Bonikowski, E. Bryniarski and U. Wybraniec, Extensions and intentions in the rough set theory, Information Sciences, 107(1998), 149-167.
[2] X. Ge and J. Qian, Some investigations on higher mathematics scores for Chinese university students, International Journal of Computer and Information Science and Engineering, 3(2009), 46-49.
[3] X. Ge, J. Li and Y. Ge, Some separations in covering approximation, International Journal of Computational and Mathematical Sciences, 4(2010), 156-160
[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] M. Kryszkiewicz, Rule in incomplete information systems, Information Sciences, 113(1998), 271-292.
[7] 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.
[8] 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.
[9] Liu M, Shao M, Zhang W X, Wu C. Reduction method for concept lattices based on rough settheory and its application Computers and Mathematics with Applications, 2007, 53: 1390-1410.
[10] Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11(1982), 341-356.
[11] Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning About Data, Kluwer Academic Publishers, 1991.
[12] Z. Pawlak, Rough classification, Int. J. Human-computer Studies, 51(1999), 369-383.
[13] D. Pei, On definable concepts of rough set models, Information Sciences, 177(2007), 4230-4239.
[14] J. A. Pomykala, Approximation operations in approximation spaces, Bull. Pol. Acad. Sci., 35(1987), 653-662.
[15] K. Qin, Y. Gao and Z. Pei, On covering rough sets, Lecture Notes in AI, 4481(2007), 34-41.
[16] Y. Yao, Views of the theory of rough sets in finite universes, International Journal of Approximate Reasoning, 15(1996), 291-317.
[17] Y. Yao, Relational interpretations of neighborhood operators and rough set approximation operators, Information Sciences, 111(1998), 239-259.
[18] Y. Yao, On generalizing rough set theory, Lecture Notes in AI, 2639(2003), 44-51.
[19] W. Zhu, Topological approaches to covering rough sets, Information Sciences, 177(2007), 1499-1508.
[20] W. Zhu, Relationship between generalized rough sets based on binary relation and covering, Information Sciences, 179(2009), 210-225.
[21] W. Zhu and F. Wang, On Three Types of Covering Rough Sets, IEEE Transactions on Knowledge and Data Engineering, 19(2007), 1131-1144.