Invariance of separation in covering approximation spaces

Qifang Li; Jinjin Li; Xun Ge; Yiliang Li; Qifang Li; Jinjin Li; Xun Ge; Yiliang Li

doi:10.3934/math.2021341

AIMS Mathematics

2021, Volume 6, Issue 6: 5772-5785. doi: 10.3934/math.2021341

Previous Article Next Article

Research article

Invariance of separation in covering approximation spaces

Qifang Li ¹,
Jinjin Li ^{1
,
,},
Xun Ge ²,
Yiliang Li ^{3
,
,}

1.
School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian 363000, China
2.
School of Mathematical Sciences, Soochow University, Suzhou, Jiangsu 215006, China
3.
School of Mathematics, Shandong University, Jinan, Shandong 250100, China

Received: 09 December 2020 Accepted: 12 March 2021 Published: 26 March 2021
MSC : 54B05, 54D65, 68U35

In this paper, the invariance of separation in covering approximation spaces are discussed. This paper proves that some separations in covering approximation spaces are invariant to reducts of coverings, invariant to covering approximation subspaces and invariant under CAP-transformations of covering approximation spaces. These results deepen and enrich theory of separations in covering approximation spaces, which is helpful to give further researches and applications of Pawlak rough set theory in information sciences.
- covering approximation space,
- invariance,
- separation,
- reduct,
- covering approximation subspace,
- transformation
Citation: Qifang Li, Jinjin Li, Xun Ge, Yiliang Li. Invariance of separation in covering approximation spaces[J]. AIMS Mathematics, 2021, 6(6): 5772-5785. doi: 10.3934/math.2021341

Related Papers:

Abstract

In this paper, the invariance of separation in covering approximation spaces are discussed. This paper proves that some separations in covering approximation spaces are invariant to reducts of coverings, invariant to covering approximation subspaces and invariant under CAP-transformations of covering approximation spaces. These results deepen and enrich theory of separations in covering approximation spaces, which is helpful to give further researches and applications of Pawlak rough set theory in information sciences.

References

[1]	Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11 (1982), 341–356.
[2]	Z. Bonikowski, E. Bryniarski, U. Wybraniec, Extensions and intentions in the rough set theory, Inform. Sciences, 107 (1998), 149–167. doi: 10.1016/S0020-0255(97)10046-9
[3]	A. Jackson, Z. Pawlak, S. LeClair, Rough sets applied to the discovery of materials knowledge, J. Alloy. Compd., 279 (1998), 14–21. doi: 10.1016/S0925-8388(98)00607-0
[4]	E. Lashin, A. Kozae, A. Khadra, T. Medhat, Rough set theory for topological spaces, Int. J. Approx. Reason., 40 (2005), 35–43. doi: 10.1016/j.ijar.2004.11.007
[5]	Z. Pawlak, Rough Sets: Theoretical aspects of reasoning about data, Springer Netherlands, 1991.
[6]	D. Pei, On definable concepts of rough set models, Inform. Sciences, 177 (2007), 4230–4239. doi: 10.1016/j.ins.2007.01.020
[7]	Y. Y. Yao, Views of the theory of rough sets in finite universes, Int. J. Approx. Reason., 15 (1996), 291–317. doi: 10.1016/S0888-613X(96)00071-0
[8]	Y. Y. Yao, Relational interpretations of neighborhood operators and rough set approximation operators, Inform. Sciences, 111 (1998), 239–259. doi: 10.1016/S0020-0255(98)10006-3
[9]	Y. Y. Yao, Three-way decision: An interpretation of rules in rough set theory, Lect. Notes Comput. Sc., 5589 (2009), 642–649. doi: 10.1007/978-3-642-02962-2_81
[10]	W. Zhu, Relationship between generalized rough sets based on binary relation and covering, Inform. Sciences, 179 (2009), 210–225. doi: 10.1016/j.ins.2008.09.015
[11]	G. Xun, On covering approximation subspaces, Computer Science Journal of Moldova, 17 (2009), 74–88.
[12]	G. Xun, An application of covering approximation spaces on network security, Comput. Math. Appl., 60 (2010), 1191–1199. doi: 10.1016/j.camwa.2010.05.043
[13]	G. Xun, L. Jinjin, G. Ying, Some separations in covering approximation spaces, International Journal of Computational and Mathematical Sciences, 4 (2010), 156–160.
[14]	M. Kondo, On the structure of generalized rough sets, Inform. Sciences, 176 (2006), 586–600.
[15]	E. Lashin, T. Medhat, Topological reduction of information systems, Chaos, Soliton. Fract., 25 (2005), 277–286. doi: 10.1016/j.chaos.2004.09.107
[16]	Y. Leung, W. Wu, W. Zhang, Knowledge acquisition in incomplete information systems: A rough set approach, Eur. J. Oper. Res., 168 (2006), 164–180. doi: 10.1016/j.ejor.2004.03.032
[17]	K. Qin, Y. Gao, Z. Pei, On covering rough sets, In: Rough Sets and Knowledge Technology, Springer, Berlin, Heidelberg, 2007, 34–41.
[18]	W. Żakowski, Approximations in the space $(U, \Pi)$, Demonstration Mathematica, 16 (1983), 761–769.
[19]	Y. Y. Yao, On generalizing rough set theory, Lect. Notes Comput. Sc., 2639 (2003), 44–51. doi: 10.1007/3-540-39205-X_6
[20]	W. Zhu, Topological approaches to covering rough sets, Inform. Sciences, 177 (2007), 1499–1508. doi: 10.1016/j.ins.2006.06.009
[21]	W. Zhu, F. Wang, Reduction and axiomization of covering generalized rongh sets, Inform. Sciences, 152 (2003), 217–230. doi: 10.1016/S0020-0255(03)00056-2
[22]	W. Zhu, F. Wang, On three types of covering rough sets, IEEE T. Knowl. Data En., 19 (2007), 1131–1144. doi: 10.1109/TKDE.2007.1044
[23]	Á. Császár, Separation axioms for generalizaed topologies, Acta Math. Hung., 104 (2004), 63–69. doi: 10.1023/B:AMHU.0000034362.97008.c6
[24]	R. Engelking, General topology: Rrevised and completed edition, Heldermann Verlag, 1989.
[25]	T. Noiri, E. Hatir, $\Lambda$sp-sets and some weak separation axioms, Acta Math. Hung., 103 (2004), 225–232. doi: 10.1023/B:AMHU.0000028409.42549.72
[26]	Z. Yun, X. Ge, X. Bai, Axiomatization and conditions for neighborhoods in a covering to form a partition, Inform. Sciences, 181 (2011), 1735–1740. doi: 10.1016/j.ins.2011.01.013
[27]	J. G. Bazan, A. Skowron, P. Synak, Dynamic reducts as a tool or extracting laws from decisions tables, In: Methodologies for Intelligent Systems, 1994,346–355.

Reader Comments

Your name:*

Email:*
© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)