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

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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.

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

[2] P. H ajek, Metamathematices of Fuzzy Logic, Kluwer Academic Publishers, Dor- drecht, 1998. Google Scholar

[3] 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

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

[5] 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

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

[7] 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

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

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

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

[11] 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

[12] 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