Definable Subsets in Covering Approximation Spaces
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:56936", author = "Xun Ge and Zhaowen Li", title = "Definable Subsets in Covering Approximation Spaces", 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.", volume = "5", number = "3", pages = "385-4", }