SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 2

A Minimal Family of Sub-bases

Yiliang Li(Minnan Normal University)0000-0002-8994-4491
Yidong Lin(Xiamen University)0000-0001-7552-5555
Jinjin Li(Minnan Normal University)0000-0001-9947-6858
Jun-e Feng(Minnan Normal University)0000-0003-3881-3042
Hongkun Wang(Georgetown University)0000-0002-5443-319X
Pages
—
Publication Date
2020-04-02
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, experiments are conducted to illustrate the effectiveness of the proposed approach.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper investigates a minimal family of sub-bases.
📊
Key Findings & Data:First, the concept of a minimal family of sub-bases is presented and its properties are studied.
💡
Conclusion & Impact:Finally, experiments are conducted to illustrate the effectiveness of the proposed approach.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:a minimal family of sub-bases · Boolean matrix · covering information systems

Abstract

This paper investigates a minimal family of sub-bases. First, the concept of a minimal family of sub-bases is presented and its properties are studied. Then the relationship between reducts in covering information systems and minimal families of sub-bases is discussed. Based on Boolean matrices, an approach is provided to derive a minimal family of sub-bases. Finally, experiments are conducted to illustrate the effectiveness of the proposed approach.

🔖

Cite This Article

Li, Y., Lin, Y., Li, J., Feng, J., Wang, H. (2020). A Minimal Family of Sub-bases. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 2. https://doi.org/10.15672/hujms.477534

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (28)

  1. R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989.
  2. J.M. Graymala-Busse, Algebraic properties of knowledge representation systems, in: Proceedings of the ACM SIGART international symposium on Methodologies for intelligent systems, ACM, 432-440, 1986.
  3. G.M. Lang, Q.G. Li and L.K. Guo, Homomorphisms-based attribute reduction of dynamic fuzzy covering information systems, Int. J. Gen. Syst. 44 (7-8), 791-811, 2015.
  4. J.J. Li, K.D. Li and S. Lin, Introduction of Basic Topology, Science Press, Beijing, 2009 (in Chinese).
  5. D.Y. Li and Y.C. Ma, Invariant characters of information systems under some homomorphisms, Inf. Sci. 129 (1-4), 211-220, 2000.
  6. J.J. Li and Y.L. Zhang, Reduction of subbases and its applications, Utilitas Math. 82 (3), 179-192, 2010.
  7. Z. Pawlak, Rough sets, Int. J. Comput. Inf. Sci. 11 (5), 341-356, 1982.
  8. T. Speer, A short study of Alexandroff spaces, at http://arxiv.org/abs/0708.2136, 2007.
  9. A.H. Tan, J.J. Li and G.P. Lin, Extended results on the relationship between information systems, Inf. Sci. 290, 156-173, 2015.
  10. A.H. Tan, J.J. Li and G.P. Lin and Y.J. Lin, Fast approach to knowledge acquistion in covering information systems using matrix operations, Knowl.-Based Syst. 79, 90-98, 2015.
  11. A.H. Tan, J.J. Li, Y.J. Lin and G.P. Lin, Matrix-based set approximations and reductions in covering decision information systems, Int. J. Approx. Reason. 59, 68-80, 2015.
  12. E.C.C. Tsang, C.Z. Wang, D.G. Chen, C.X. Wu and Q.H. Hu, Communication between information systems using fuzzy rough sets, IEEE Trans. Fuzzy syst. 21 (3), 527-540, 2013.
  13. C.Z. Wang, W.Y. Bao, X.X. Wang and Q. He, A mapping between fuzzy covering information systems, Proc. 2013 IEEE International Conference on Granular Computing, 315-319.
  14. C.Z.Wang, D.G. Chen and Q.H. Hu, Some invariant properties of ordered information systems under homomorphism, Sci. China: Inf. Sci. 53 (9), 1816-1825, 2010.
  15. C.Z. Wang, D.G. Chen and Q.H. Hu, Fuzzy information systems and their homomorphisms, Fuzzy Sets Syst. 249, 128-138, 2014.
  16. C.Z. Wang, D.G. Chen, B.Q. Sun and Q.H. Hu, Communication between information systems with covering based rough sets, Inf. Sci. 216, 17-33, 2012.
  17. C.Z. Wang, D.G. Chen, C. Wu and Q.H. Hu, Data compression with homomorphism in covering information systems, Int. J. Approx. Reason. 52 (4), 519-525, 2011.
  18. C.Z. Wang, D.G. Chen and L.K. Zhu, Homomorphisms between fuzzy information systems, Appl. Math. Lett. 22 (7), 1045-1050, 2009.
  19. C.Z. Wang, C.X. Wu, D.G. Chen and W.J. Du, Some properties of relation information systems under homomorphisms, Appl. Math. Lett. 21 (9), 940-945, 2008.
  20. C.Z. Wang, C.X. Wu, D.G. Chen, Q.H. Hu and C. Wu, Communicating between information systems, Inf. Sci. 178 (16), 3228-3239, 2008.
  21. W. Żakowski, Approximations in the space (U, Π), Demonstr. Math. 16 (3), 761-769, 1983.
  22. X.D. Zhang, Matrix analysis and applications, Tsinghua University Press, Beijing, 2004 (in Chinese).
  23. P. Zhu, Covering rough sets based on neighborhoods: An approach without using neighborhoods, Int. J. Approx. Reason. 52 (3), 461-472, 2011.
  24. P. Zhu and Q.Y. Wen, Some improved results on communication between information systems, Inf. Sci. 180 (18), 3521-3531, 2010.
  25. P. Zhu and Q.Y. Wen, Homomorphisms between fuzzy information systems revisited, Appl. Math. Lett. 24 (9), 1548-1553, 2011.
  26. P. Zhu and Q.Y. Wen, A note on communicating between information systems based on including degrees, Int. J. Gen. Syst. 40 (8), 837-840, 2011.
  27. P. Zhu, H.Y. Xie and Q.Y. Wen, A unified definition of consistent functions, Fund. Inf. 135 (3), 331-340, 2014.
  28. P. Zhu, H.Y. Xie and Q.Y. Wen, A unified view of consistent functions, Soft Comput. 21 (9), 2189-2199, 2017.