Sub-base local reduct in a family of sub-bases

Liying Yang; Jinjin Li; Yiliang Li; Qifang Li; Liying Yang; Jinjin Li; Yiliang Li; Qifang Li

doi:10.3934/math.2022732

AIMS Mathematics

2022, Volume 7, Issue 7: 13271-13277. doi: 10.3934/math.2022732

Previous Article Next Article

Research article

Sub-base local reduct in a family of sub-bases

1.
Department of Teacher Education, Zhangzhou City College, Zhangzhou, Fujian 363000, China
2.
School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian 363000, China
3.
School of Mathematics, Shandong University, Jinan, Shandong 250100, China

Received: 15 January 2022 Revised: 26 April 2022 Accepted: 05 May 2022 Published: 13 May 2022
MSC : 54A05, 54B15, 54C05, 54C10

This paper discusses sub-base local reducts in a family of sub-bases. Firstly, definitions of sub-base local consistent sets and sub-base local reducts are provided. Using the sub-base local discernibility matrix, a necessary and sufficient condition for sub-base local consistent sets is presented. Secondly, properties of the sub-base local core are studied. Finally, sub-base local discernibility Boolean matrices are defined, and the calculation method is given. Utilizing sub-base local discernibility Boolean matrices, an algorithm is devised to obtain sub-base local reducts.
- sub-base local reduct,
- sub-base local consistent set,
- sub-base local discernibility matrix,
- sub-base local discernibility Boolean matrix
Citation: Liying Yang, Jinjin Li, Yiliang Li, Qifang Li. Sub-base local reduct in a family of sub-bases[J]. AIMS Mathematics, 2022, 7(7): 13271-13277. doi: 10.3934/math.2022732

Related Papers:

Abstract

This paper discusses sub-base local reducts in a family of sub-bases. Firstly, definitions of sub-base local consistent sets and sub-base local reducts are provided. Using the sub-base local discernibility matrix, a necessary and sufficient condition for sub-base local consistent sets is presented. Secondly, properties of the sub-base local core are studied. Finally, sub-base local discernibility Boolean matrices are defined, and the calculation method is given. Utilizing sub-base local discernibility Boolean matrices, an algorithm is devised to obtain sub-base local reducts.

References

[1]	Z. Pawlak, Rough sets, Int. J. Comput. Inf. Sci., 11 (1982), 341–356. https://doi.org/10.1007/BF01001956
[2]	A. Campagner, D. Ciucci, T. Denœux, Belief functions and rough sets: Survey and new insights, Int. J. Approx. Reason., 143 (2022), 192–215. https://doi.org/10.1016/j.ijar.2022.01.011 doi: 10.1016/j.ijar.2022.01.011
[3]	W. Żakowski, Approximations in the space (U,), Demonstr. Math. 16 (1983), 761–769.
[4]	A. H. Tan, J. J. Li, Y. J. Lin, G. P. Lin, Matrix-based set approximations and reductions in covering decision information systems, Int. J. Approx. Reason., 59 (2015), 68–80. https://doi.org/10.1016/j.ijar.2015.01.006 doi: 10.1016/j.ijar.2015.01.006
[5]	A. H. Tan, J. J. Li, G. P. Lin, Y. J. Lin, Fast approach to knowledge acquisition in covering information systems using matrix operations, Knowl. Based Syst., 79 (2015), 90–98. https://doi.org/10.1016/j.knosys.2015.02.003 doi: 10.1016/j.knosys.2015.02.003
[6]	D. G. Chen, C. Z. Wang, Q. H. Hu, A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets, Inf. Sci., 177 (2007), 3500–3518. https://doi.org/10.1016/j.ins.2007.02.041 doi: 10.1016/j.ins.2007.02.041
[7]	C. Z. Zhong, Q. He, D. G. Cheng, Q. H. Hu, A novel method for attribute reduction of covering decision systems, Inf. Sci., 254 (2014), 181–196. https://doi.org/10.1016/j.ins.2013.08.057 doi: 10.1016/j.ins.2013.08.057
[8]	T. Yang, Q. G. Li, B. L. Zhou, Related family: A new method for attribute reduction of covering information systems, Inf. Sci., 228 (2013), 175–191. https://doi.org/10.1016/j.ins.2012.11.005 doi: 10.1016/j.ins.2012.11.005
[9]	Q. F. Li, J. J. Li, X. Ge, Y. L. Li, Invariance of separation in covering approximation spaces, AIMS Math., 6 (2021), 5772–5785. https://doi.org/10.3934/math.2021341 doi: 10.3934/math.2021341
[10]	P. K. Singh, S. Tiwari, Topological structures in rough set theory: A survey, Hacett. J. Math. Stat., 49 (2020), 1270–1294.
[11]	R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989.
[12]	J. J. Li, Y. L. Zhang, Reduction of subbases and its applications, Utilitas Math., 82 (2010), 179–192.
[13]	Y. L. Li, J. J. Li, Y. D. Lin, J. E. Feng, H. K. Wang, A minimal family of sub-bases, Hacett. J. Math. Stat., 49 (2019), 793–807.
[14]	Y. D. Lin, J. J. Li, L. X. Peng, Z. Q. Feng, Minimal base for finite topological space by matrix method, Fund. Inform., 174 (2020), 167–173. https://doi.org/10.3233/FI-2020-1937 doi: 10.3233/FI-2020-1937
[15]	Y. L. Li, J. J. Li, H. K. Wang, Minimal bases and minimal sub-bases for topological spaces, Filomat., 33 (2019), 1957–1965. https://doi.org/10.2298/FIL1907957L doi: 10.2298/FIL1907957L
[16]	X. D. Zhang, Matrix analysis and applications, Tsinghua University Press, Beijing, 2004 (in Chinese).

Reader Comments

Your name:*

Email:*
© 2022 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)