DOI QR코드

DOI QR Code

FUZZY CONNECTIONS ON ADJOINT TRIPLES

  • Ko, Jung Mi (Department of Mathematics Gangneung-Wonju National) ;
  • Kim, Yong Chan (Department of Mathematics Gangneung-Wonju National)
  • Received : 2019.08.28
  • Accepted : 2019.12.03
  • Published : 2019.12.30

Abstract

In this paper, we introduce the notion of residuated and Galois connections on adjoint triples and investigate their properties. Using the properties of residuated and Galois connections, we solve fuzzy relation equations and give their examples.

Keywords

References

  1. A.A. Abdel-Hamid, N.N. Morsi, Associatively tied implications, Fuzzy Sets and Systems, 136 (3) (2003), 291-311. https://doi.org/10.1016/S0165-0114(02)00268-3
  2. R. Belohlavek, Fuzzy Relational Systems, Kluwer Academic Publishers, New York, 2002.
  3. M.E. Cornejo, J. Medina, E. Ramirez, A comparative study of adjoint triples, Fuzzy Sets and Systems, 211 (2013), 1-14. https://doi.org/10.1016/j.fss.2012.05.004
  4. M.E. Cornejo, J. Medina and E. Ramirez, Multi-adjoint algebras versus non-commutative residuated structures, International Journal of Approximate Reasoning 66 (2015), 119-138. https://doi.org/10.1016/j.ijar.2015.08.003
  5. N. Madrid, M. Ojeda-Aciego, J. Medina and I. Perfilieva, L-fuzzy relational mathematical morphology based on adjoint triples, Information Sciences 474 (2019), 75-89. https://doi.org/10.1016/j.ins.2018.09.028
  6. P. Hajek, Metamathematices of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998.
  7. U. Hohle, E.P. Klement, Non-classical logic and their applications to fuzzy subsets, Kluwer Academic Publishers, Boston, 1995.
  8. 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.
  9. 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
  10. M. Kryszkiewicz, Rough set approach to incomplete information systems, Information Sciences 112 (1998), 39-49. https://doi.org/10.1016/S0020-0255(98)10019-1
  11. Z. Pawlak, Rough sets, Internat. J. Comput. Inform. Sci., 11 (1982), 341-356. https://doi.org/10.1007/BF01001956
  12. Z. Pawlak, Rough sets: Theoretical Aspects of Reasoning about Data, System Theory, Knowledge Engineering and Problem Solving, Kluwer Academic Publishers, Dordrecht, The Netherlands (1991)
  13. I. Perfilieva, Finitary solvability conditions for systems of fuzzy relation equations, Information Sciences, 234 (2013), 29-43. https://doi.org/10.1016/j.ins.2011.04.035
  14. I. Perfilieva and L. Noskova, System of fuzzy relation equations with infcomposition: Commplete set of solutions, Fuzzy Sets and Systems 159 (2008), 2256-2271. https://doi.org/10.1016/j.fss.2007.12.012
  15. E. Sanchez, Resolution of composite fuzzy relation equations, Inform. and Control 30 (1976), 38-48. https://doi.org/10.1016/S0019-9958(76)90446-0
  16. B.S. Shieh, Solutions of fuzzy relation equations based on continuous t-norms, Information Sciences, 177 (2007), 4208-4215. https://doi.org/10.1016/j.ins.2007.04.006
  17. P. Sussner, Lattice fuzzy transforms from the perspective of mathematical morphology, Fuzzy Sets and Systems, 288 (2016), 115-128. https://doi.org/10.1016/j.fss.2015.09.018
  18. S. P. Tiwari, I. Perfilieva and A.P. Singh, Generalized residuated lattices based F-transformation, Iranian Journal of Fuzzy Systems 15 (2) (2018), 165-182.
  19. 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