Commenced in January 2007
Paper Count: 31824
On an Open Problem for Definable Subsets of Covering Approximation Spaces
Abstract:Let (U;D) be a Gr-covering approximation space (U; C) with covering lower approximation operator D and covering upper approximation operator D. For a subset X of U, this paper investigates the following three conditions: (1) X is a definable subset of (U;D); (2) X is an inner definable subset of (U;D); (3) X is an outer definable subset of (U;D). It is proved that if one of the above three conditions holds, then the others hold. These results give a positive answer of an open problem for definable subsets of covering approximation spaces.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1333078Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 988
 Z. Bonikowski, E. Bryniarski and U. Wybraniec, Extensions and intentions in the rough set theory, Information Sciences, 107(1998), 149-167.
 X. Ge, Further investigations on higher mathematics scores for Chinese university students, International Journal of Computational and Mathematical Sciences, 3(2009), 181-185.
 X. Ge, An application of covering approximation spaces on network security, Computers and Mathematics with Applications, 60(2010), 1191- 1199.
 X. Ge, J. Li and Y. Ge, Some separations in covering approximation, International Journal of Computational and Mathematical Sciences, 4(2010), 156-160.
 X. Ge and Z. Li, Definable subsets in covering approximation spaces, International Journal of Computational and Mathematical Sciences, 5(2011), 31-34.
 X. Ge and J. Qian, Some investigations on higher mathematics scores for Chinese university students, International Journal of Computer and Information Engineering, 3(2009), 209-212.
 E. Lashin, A. Kozae, A. Khadra and T. Medhat, Rough set theory for topological spaces, International Journal of Approximate Reasoning, 40(2005), 35-43.
 Z. Pawlak, Rough sets, International journal of computer and information science, 11(1982), 341-356.
 Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning About Data, Kluwer Academic Publishers, 1991.
 Z. Pawlak, Rough classification, International journal of Humancomputer Studies, 51(1999), 369-383.
 Z. Pawlak and A. Skowron, Rudiments of rough sets, Information Sciences, 177(2007), 3-27.
 Z. Pawlak and A. Skowron, Rough sets: Some extensions, Information Sciences, 177(2007), 28-40.
 Z. Pawlak and A. Skowron, Rough sets and Boolean reasoning, Information Sciences, 177(2007), 41-73.
 D. Pei, On definable concepts of rough set models, Information Sciences, 177(2007), 4230-4239.
 J. A. Pomykala, Approximation operations in approximation spaces, Bull. Pol. Acad. Sci., 35(1987), 653-662.
 K. Qin, Y. Gao and Z. Pei, On covering rough sets, Lecture Notes in Artificial Intelligence, 4481(2007), 34-41.
 P. Samanta and M. Chakraborty, Covering based approaches to rough sets and implication lattices, Lecture Notes in Artificial Intelligence, 5908(2009), 127-134.
 Y. Yao, Views of the theory of rough sets in finite universes, International Journal of Approximate Reasoning, 15(1996), 291-317.
 Y. Yao, Relational interpretations of neighborhood operators and rough set approximation operators, Information Sciences, 111(1998), 239-259.
 Y. Yao, On generalizing rough set theory, Lecture Notes in AI, 2639(2003), 44-51.
 Z. Yun, Xun Ge and X. Bai, Axiomatization and conditions for neighborhoods in a covering to form a partition, Information Sciences, (2011), doi:10.1016/j.ins.2011.01.013.
 W. Zakowski, Approximations in the Space (u, ╬á), Demonstratio Mathematica, 16(1983), 761-769.
 W. Zhu, Topological approaches to covering rough sets, Information Sciences, 177(2007), 1499-1508.
 W. Zhu, Relationship between generalized rough sets based on binary relation and covering, Information Sciences, 179(2009), 210-225.
 W. Zhu and F. Wang, Reduction and axiomatization of covering generalized rough sets, Information Sciences, 152(2003), 217-230.
 W. Zhu and F. Wang, On Three Types of Covering Rough Sets, IEEE Transactions on Knowledge and Data Engineering, 19(2007), 1131-1144.