Korean J. Math.  Vol 22, No 3 (2014)  pp.553-565
DOI: https://doi.org/10.11568/kjm.2014.22.3.553

Join-meet approximation operators induced by Alexandrov fuzzy topologies

Yong Chan Kim


In this paper, we investigate the properties of Alexandrov fuzzy topologies and join-meet  approximation operators.  We study fuzzy preorder, Alexandrov topologies join-meet  approximation operators induced by Alexandrov fuzzy topologies. We give their examples.


Complete residuated lattices, fuzzy preorder, join-meet approximation operators, Alexandrov (fuzzy) topologies

Subject classification

03E72, 03G10, 06A15, 54F05


Full Text:



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

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

U. H ̈ohle and S.E. Rodabaugh, Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The Handbooks of Fuzzy Sets Series 3, Kluwer Academic Publishers, Boston. (Google Scholar)

Fang Jinming, I-fuzzy Alexandrov topologies and specialization orders, Fuzzy Sets and Systems, 158 (2007), 2359–2374. (Google Scholar)

Y.C. Kim, Alexandrov L-topologies and L-join meet approximation operators, International Journal of Pure and Applied Mathematics, 91 (1) (2014), 113– 129. (Google Scholar)

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

H. Lai and D. Zhang, Concept lattices of fuzzy contexts: Formal concept analysis vs. rough set theory, Int. J. Approx. Reasoning 50 (2009), 695–707. (Google Scholar)

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

Z. Pawlak, Rough probability, Bull. Pol. Acad. Sci. Math. 32 (1984), 607–615. (Google Scholar)

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

Y.H. She and 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)

Zhen Ming Ma and Bao Qing Hu, Topological and lattice structures of L-fuzzy rough set determined by lower and upper sets, Information Sciences 218 (2013), 194–204. (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