Korean Journal of Mathematics

  • 제28권2호
  • /
  • Pages.311-321
  • /
  • 2020
  • /
  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

THE PROPERTIES OF RESIDUATED CONNECTIONS AND ALEXANDROV TOPOLOGIES

  • Oh, Ju-Mok (Department of Mathematics Gangneung-Wonju National) ;
  • Kim, Yong Chan (Department of Mathematics Gangneung-Wonju National)
  • 투고 : 2020.01.10
  • 심사 : 2020.06.17
  • 발행 : 2020.06.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we investigate the properties of residuated connections and Alexandrov topologies based on [0, ∞]. Under various relations, we investigate the residuated and dual residuated connections on Alexandrov toplogies. Moreover, we study their properties and give their examples.

키워드

참고문헌

  1. R. Belohlavek, Fuzzy Relational Systems, Kluwer Academic Publishers, New York, 2002.
  2. T.S. Blyth, M.F. Janovitz, Residuation Theory, Pergamon Press, New York, 1972.
  3. Y.C. Kim, Join-meet preserving maps and fuzzy preorders, Journal of Intelligent & Fuzzy Systems 28(2015), 1089-1097. https://doi.org/10.3233/IFS-141392
  4. Y.C. Kim, Categories of fuzzy preorders, approximation operators and Alexandrov topologies, Journal of Intelligent & Fuzzy Systems 31 (2016), 1787-1793. https://doi.org/10.3233/JIFS-152398
  5. 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
  6. Z.M. Ma, B.Q. Hu, Topological and lattice structures of L-fuzzy rough set determined by lower and upper sets, Inf. Sci. 218 (2013), 194-204. https://doi.org/10.1016/j.ins.2012.06.029
  7. E. Or lowska,I. Rewitzky, Context algebras, context frames and their discrete duality, Transactions on Rough Sets IX, Springer, Berlin, 2008, 212-229.
  8. E. Or lowska, I. Rewitzky Algebras for Galois-style connections and their discrete duality, Fuzzy Sets and Systems, 161 (2010), 1325-1342. https://doi.org/10.1016/j.fss.2009.12.013
  9. Z. Pawlak, Rough sets, Internat. J. Comput. Inform. Sci. 11 (1982), 341-356. https://doi.org/10.1007/BF01001956
  10. Z. Pawlak, Rough sets: Theoretical Aspects of Reasoning about Data, System Theory, Knowledge Engineering and Problem Solving, Kluwer Academic Publishers, Dordrecht, The Netherlands (1991).
  11. A. M. Radzikowska, E.E. Kerre, A comparative study of fuzy rough sets, Fuzzy Sets and Systems, 126 (2002), 137-155. https://doi.org/10.1016/S0165-0114(01)00032-X
  12. Y.H. She, G.J. Wang, An axiomatic approach of fuzzy rough sets based on residuated lattices, Computers and Mathematics with Applications, 58 (2009), 189-201. https://doi.org/10.1016/j.camwa.2009.03.100
  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