[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
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.
[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.
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.