Korean J. Math.  Vol 27, No 4 (2019)  pp.1109-1118
DOI: https://doi.org/10.11568/kjm.2019.27.4.1109

Fuzzy connections on adjoint triples

Jung Mi Ko, Yong Chan Kim


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.


03E72, 03G10, 06A15, 54F05

Subject classification


This work was supported by the Research Institute of Natural Science of Gangneung-Wonju National University.

Full Text:



A.A. Abdel-Hamid, N.N. Morsi, Associatively tied implications, Fuzzy Sets and Systems, 136 (3) (2003), 291–311. (Google Scholar)

R. Bˇelohl ́avek, Fuzzy Relational Systems, Kluwer Academic Publishers, New York, 2002. (Google Scholar)

M.E. Cornejo, J. Medina, E. Ram ́ırez, A comparative study of adjoint triples, Fuzzy Sets and Systems, 211 (2013), 1–14. (Google Scholar)

M.E. Cornejo, J. Medina and E. Ram ́ırez, Multi-adjoint algebras versus non-commutative residuated structures, International Journal of Approximate Reasoning 66 (2015), 119-138. (Google Scholar)

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. (Google Scholar)

P. H ́ajek, Metamathematices of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998. (Google Scholar)

U. H ̈ohle, E.P. Klement, Non-classical logic and their applications to fuzzy subsets, Kluwer Academic Publishers, Boston, 1995. (Google Scholar)

U. H ̈ohle, S.E. Rodabaugh, Mathematics of Fuzzy Sets, Logic, Topology and Measure Theory, The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers, Dordrecht, 1999. (Google Scholar)

Y.C. Kim, Join-meet preserving maps and Alexandrov fuzzy topologies, Journal of Intelligent and Fuzzy Systems 28 (2015), 457–467. (Google Scholar)

M. Kryszkiewicz, Rough set approach to incomplete information systems, Information Sciences 112 (1998), 39–49. (Google Scholar)

Z. Pawlak, Rough sets, Internat. J. Comput. Inform. Sci., 11 (1982), 341–356. (Google Scholar)

Z. Pawlak, Rough sets: Theoretical Aspects of Reasoning about Data, System Theory, Knowledge Engineering and Problem Solving, Kluwer Academic Publishers, Dordrecht, The Netherlands (1991) (Google Scholar)

I. Perfilieva, Finitary solvability conditions for systems of fuzzy relation equations, Information Sciences, 234 (2013), 29–43. (Google Scholar)

I. Perfilieva and L. Noskova, System of fuzzy relation equations with inf- composition: Commplete set of solutions, Fuzzy Sets and Systems 159 (2008), 2256–2271. (Google Scholar)

E. Sanchez, Resolution of composite fuzzy relation equations, Inform. and Control 30 (1976), 38–48. (Google Scholar)

B.S. Shieh, Solutions of fuzzy relation equations based on continuous t-norms, Information Sciences, 177 (2007), 4208-4215. (Google Scholar)

P. Sussner, Lattice fuzzy transforms from the perspective of mathematical morphology, Fuzzy Sets and Systems, 288 (2016), 115–128. (Google Scholar)

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. (Google Scholar)

M. Ward, R.P. Dilworth, Residuated lattices, Trans. Amer. Math. Soc. 45 (1939), 335–354, (Google Scholar)


  • There are currently no refbacks.

ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr