International Journal of Fuzzy Logic and Intelligent Systems

Korean Institute of Intelligent Systems (한국지능시스템학회)
권호 표지
DOI QR코드

DOI QR Code

Galois and Residuated Connections on Sets and Power Sets

  • Kim, Yong-Chan (Department of Mathematics, Gangneung-Wonju National University) ;
  • Ko, Jung-Mi (Department of Mathematics, Gangneung-Wonju National University)
  • Received : 2010.11.14
  • Accepted : 2011.05.27
  • Published : 2011.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

We investigate the relations between various connections on set and those on power set. Moreover, we give their examples.

Keywords

References

  1. R. Belohlavek, "Similarity relations in concept lattices," J. Logic and Computation, vol. 10, no 6, pp. 823-845, 2000. https://doi.org/10.1093/logcom/10.6.823
  2. R. Belohlavek, "Lattices of fixed points of Galois connections," Math. Logic Quart., vol. 47, pp. 111-116, 2001. https://doi.org/10.1002/1521-3870(200101)47:1<111::AID-MALQ111>3.0.CO;2-A
  3. R. Belohlavek, "Concept lattices and order in fuzzy logic," Ann. Pure Appl. Logic, vol. 128, pp.277-298, 2004. https://doi.org/10.1016/j.apal.2003.01.001
  4. R. Belohlavek, Fuzzy relational systems, Kluwer Academic Publisher, New York, 2002.
  5. G. Georgescu, A. Popescue," Non-dual fuzzy connections," Arch. Math. Log., vol. 43, pp. 1009-1039, 2004. https://doi.org/10.1007/s00153-004-0240-4
  6. J.G. Garcia, I.M. Perez, M.A.P. Vicente, D. Zhang," Fuzzy Galois connections categorically," Math. Log. Quart., vol. 56, pp. 131-147, 2010. https://doi.org/10.1002/malq.200810044
  7. H. Lai, D. Zhang," Concept lattices of fuzzy contexts: Formal concept analysis vs. rough set theory," Int. J. Approx. Reasoning, vol. 50, pp.695-707, 2009. https://doi.org/10.1016/j.ijar.2008.12.002
  8. Y.C. Kim, J.W. Park, "Join preserving maps and various concepts," Int.J. Contemp. Math. Sciences, vol. 5, no.5, pp.243-251, 2010.
  9. J.M. Ko, Y.C. Kim, "Various connections and their relations," submit to Int. J. Fuzzy Logic and Intelligent Systems.
  10. Ewa. Orlowska, I. Rewitzky, "Algebras for Galoisstyle connections and their discrete duality," Fuzzy Sets and Systems, vol.161, pp.1325-1342, 2010. https://doi.org/10.1016/j.fss.2009.12.013
  11. R. Wille, Restructuring lattice theory; an approach based on hierarchies of concept, in: 1. Rival(Ed.), Ordered Sets, Reidel, Dordrecht, Boston, 1982.
  12. Wei Yao, Ling-Xia Lu," Fuzzy Galois connections on fuzzy posets," Math. Log. Quart., vol. 55, pp. 105-112, 2009. https://doi.org/10.1002/malq.200710079