Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

FUZZY JOIN AND MEET PRESERVING MAPS ON ALEXANDROV L-PRETOPOLOGIES

  • KO, JUNG MI (Department of Mathematics, Gangneung-Wonju University) ;
  • KIM, YONG CHAN (Department of Mathematics, Gangneung-Wonju University)
  • Received : 2019.11.22
  • Accepted : 2019.12.15
  • Published : 2020.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

We introduce the concepts of fuzzy join-complete lattices and Alexandrov L-pre-topologies in complete residuated lattices. We investigate the properties of fuzzy join-complete lattices on Alexandrov L-pre-topologies and fuzzy meet-complete lattices on Alexandrov L-pre-cotopologies. Moreover, we give their examples.

Keywords

References

  1. R. Belohlavek, Fuzzy Relational Systems, Kluwer Academic Publishers, New York, 2002.
  2. L.Fan, A new approach to quantitative domain theory, Electronic Notes in Theoretic Computer Science 45 (2011).
  3. P. Hajek, Metamathematices of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998.
  4. U. Hohle, E.P. Klement, Non-classical logic and their applications to fuzzy subsets, Kluwer Academic Publishers, Boston, 1995.
  5. U. Hohle, S.E. Rodabaugh, Mathematics of Fuzzy Sets, Logic, Topology and Measure Theory, The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers, Dordrecht, 1999.
  6. 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
  7. 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
  8. 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
  9. Y.C. Kim, J.M. Ko, Images and preimages of filterbases, Fuzzy Sets and Systems 157 (2006), 1913-1927. https://doi.org/10.1016/j.fss.2005.12.012
  10. 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
  11. S.E. Rodabaugh, E.P. Klement, Topological and Algebraic Structures In Fuzzy Sets, The Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Kluwer Academic Publishers, Boston, Dordrecht, London, 2003.
  12. 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
  13. M. Ward, R.P. Dilworth, Residuated lattices, Trans. Amer. Math. Soc. 45 (1939), 335-354. https://doi.org/10.1090/S0002-9947-1939-1501995-3
  14. D. Zhang, An enriched category approach to many valued topology, Fuzzy Sets and Systems 158 (2007), 349-366. https://doi.org/10.1016/j.fss.2006.10.001
  15. W.X. Xie, Q.Y. Zhang, L. Fan, Fuzzy complete lattices, Fuzzy Sets and Systems 160 (2009), 2275-2291. https://doi.org/10.1016/j.fss.2008.12.001
  16. Q.Y. Zhang, Algebraic generations of some fuzzy powerset operators, Iranian Journal of Fuzzy systems 8 (2011), 31-58.
  17. Q.Y. Zhang, L. Fan, Continuity in quantitive domains, Fuzzy Sets and Systems 154 (2005), 118-131. https://doi.org/10.1016/j.fss.2005.01.007
  18. Q.Y. Zhang, W.X. Xie, , L. Fan, The Dedekind-MacNeille completion for fuzzy posets, Fuzzy Sets and Systems 160 (2009), 2292-2316. https://doi.org/10.1016/j.fss.2008.12.002