Research Article
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Year 2020, Volume: 49 Issue: 2, 793 - 807, 02.04.2020
https://doi.org/10.15672/hujms.477534

Abstract

References

  • [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.

A Minimal Family of Sub-bases

Year 2020, Volume: 49 Issue: 2, 793 - 807, 02.04.2020
https://doi.org/10.15672/hujms.477534

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.

References

  • [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.
There are 28 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Yiliang Li 0000-0002-8994-4491

Yidong Lin This is me 0000-0001-7552-5555

Jinjin Li This is me 0000-0001-9947-6858

Jun-e Feng This is me 0000-0003-3881-3042

Hongkun Wang This is me 0000-0002-5443-319X

Publication Date April 2, 2020
Published in Issue Year 2020 Volume: 49 Issue: 2

Cite

APA Li, Y., Lin, Y., Li, J., Feng, J.-e., et al. (2020). A Minimal Family of Sub-bases. Hacettepe Journal of Mathematics and Statistics, 49(2), 793-807. https://doi.org/10.15672/hujms.477534
AMA Li Y, Lin Y, Li J, Feng Je, Wang H. A Minimal Family of Sub-bases. Hacettepe Journal of Mathematics and Statistics. April 2020;49(2):793-807. doi:10.15672/hujms.477534
Chicago Li, Yiliang, Yidong Lin, Jinjin Li, Jun-e Feng, and Hongkun Wang. “A Minimal Family of Sub-Bases”. Hacettepe Journal of Mathematics and Statistics 49, no. 2 (April 2020): 793-807. https://doi.org/10.15672/hujms.477534.
EndNote Li Y, Lin Y, Li J, Feng J-e, Wang H (April 1, 2020) A Minimal Family of Sub-bases. Hacettepe Journal of Mathematics and Statistics 49 2 793–807.
IEEE Y. Li, Y. Lin, J. Li, J.-e. Feng, and H. Wang, “A Minimal Family of Sub-bases”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 2, pp. 793–807, 2020, doi: 10.15672/hujms.477534.
ISNAD Li, Yiliang et al. “A Minimal Family of Sub-Bases”. Hacettepe Journal of Mathematics and Statistics 49/2 (April 2020), 793-807. https://doi.org/10.15672/hujms.477534.
JAMA Li Y, Lin Y, Li J, Feng J-e, Wang H. A Minimal Family of Sub-bases. Hacettepe Journal of Mathematics and Statistics. 2020;49:793–807.
MLA Li, Yiliang et al. “A Minimal Family of Sub-Bases”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 2, 2020, pp. 793-07, doi:10.15672/hujms.477534.
Vancouver Li Y, Lin Y, Li J, Feng J-e, Wang H. A Minimal Family of Sub-bases. Hacettepe Journal of Mathematics and Statistics. 2020;49(2):793-807.