Korean J. Math. Vol. 28 No. 2 (2020) pp.311-321
DOI: https://doi.org/10.11568/kjm.2020.28.2.311

The properties of residuated connections and Alexandrov topologies

Main Article Content

Ju-mok Oh
Yong Chan Kim


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

Article Details

Supporting Agencies

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


[1] R. BVelohl avek, Fuzzy Relational Systems, Kluwer Academic Publishers, New York, 2002. Google Scholar

[2] T.S. Blyth, M.F. Janovitz, Residuation Theory, Pergamon Press, New York, 1972. Google Scholar

[3] Y.C. Kim, Join-meet preserving maps and fuzzy preorders, Journal of Intelligent & Fuzzy Systems 28(2015), 1089–1097. Google Scholar

[4] Y.C. Kim, Categories of fuzzy preorders, approximation operators and Alexandrov topologies, Journal of Intelligent & Fuzzy Systems 31 (2016), 1787–1793. Google Scholar

[5] H. Lai, D. Zhang, Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems 157 (2006), 1865–1885. Google Scholar

[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. Google Scholar

[7] E. Orlowska,I. Rewitzky, Context algebras, context frames and their discrete duality, Transactions on Rough Sets IX, Springer, Berlin, 2008, 212–229. Google Scholar

[8] E. Orlowska, I. Rewitzky Algebras for Galois-style connections and their discrete duality, Fuzzy Sets and Systems, 161 (2010), 1325–1342. Google Scholar

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

[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). Google Scholar

[11] A. M. Radzikowska, E.E. Kerre, A comparative study of fuzy rough sets, Fuzzy Sets and Systems, 126 (2002), 137–155. Google Scholar

[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. Google Scholar

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