The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

ALEXANDROV TOPOLOGIES AND NON-SYMMETRIC PSEUDO-METRICS

  • Oh, Ju-mok (Mathematics Department, Gangneung-Wonju National University) ;
  • Kim, Yong Chan (Mathematics Department, Gangneung-Wonju National University)
  • Received : 2020.01.01
  • Accepted : 2020.03.05
  • Published : 2020.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we investigate the properties of Alexandrov topologies, non-symmetric pseudo-metrics and lower approximation operators on [0, ∞]. Moreover, we investigate the relations among Alexandrov topologies, non-symmetric pseudo-metrics and lower approximation operators. We give their examples.

Keywords

References

  1. R. Belohlavek: Fuzzy Relational Systems, Kluwer Academic Publishers, New York, 2002.
  2. P. Chen & D. Zhang: Alexandroff co-topological spaces. Fuzzy Sets and Systems 161 (2010), no. 8, 2505-2514. https://doi.org/10.1016/j.fss.2010.01.002
  3. P. Hajek: Metamathematices of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht, 1998.
  4. U. Hohle & S.E. Rodabaugh: Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory. The Handbooks of Fuzzy Sets Series 3, Kluwer Academic Publishers, Boston, 1999.
  5. F. Jinming: I-fuzzy Alexandrov topologies and specialization orders. Fuzzy Sets and Systems 158 (2007), 2359-2374. https://doi.org/10.1016/j.fss.2007.05.001
  6. Y.C. Kim: Alexandrov L-topologies International Journal of Pure and Applied Mathematics. 93 (2014), no. 2, 165-179.
  7. Y.C. Kim: Join preserving maps, fuzzy preorders and Alexandrov fuzzy topologies. International Journal of Pure and Applied Mathematics, 92 (2014), no. 5, 703-718.
  8. Y.C. Kim: Join-meet preserving maps and Alexandrov fuzzy topologies. Journal of Intelligent and Fuzzy Systems 28 (2015), 457-467. https://doi.org/10.3233/IFS-141322
  9. Y.C. Kim: Join-meet preserving maps and fuzzy preorders. Journal of Intelligent and Fuzzy Systems 28 (2015), 1089-1097. https://doi.org/10.3233/IFS-141392
  10. Y.C. Kim: Categories of fuzzy preorders, approximation operators and Alexandrov topologies. Journal of Intelligent and Fuzzy Systems 31 (2016), 1787-1793. https://doi.org/10.3233/JIFS-152398
  11. H. Lai & D. Zhang: Fuzzy preorder and fuzzy topology. Fuzzy Sets and Systems 157 (2006), 1865-1885. https://doi.org/10.1016/j.fss.2006.02.013
  12. Z. Pawlak: Rough sets. Int. J. Comput. Inf. Sci. 11 (1982), 341-356. https://doi.org/10.1007/BF01001956
  13. Z. Pawlak: Rough probability. Bull. Pol. Acad. Sci. Math. 32 (1984), 607-615.
  14. S.P. Tiwari & A.K. Srivastava: Fuzzy rough sets, fuzzy preorders and fuzzy topologies. Fuzzy Sets and Systems 210 (2013), 63-68. https://doi.org/10.1016/j.fss.2012.06.001
  15. Z.M. Ma & B.Q. Hu: Topological and lattice structures of L-fuzzy rough set determined by lower and upper sets. Information Sciences 218 (2013), 194-204. https://doi.org/10.1016/j.ins.2012.06.029