Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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JOIN-MEET APPROXIMATION OPERATORS INDUCED BY ALEXANDROV FUZZY TOPOLOGIES

  • Received : 2014.03.23
  • Accepted : 2014.09.22
  • Published : 2014.09.30
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Abstract

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.

Keywords

References

  1. R. Belohlavek, Fuzzy Relational Systems, Kluwer Academic Publishers, New York , 2002.
  2. P. Hajek, Metamathematices of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998.
  3. U. Hohle and S.E. Rodabaugh, Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The Handbooks of Fuzzy Sets Series 3, Kluwer Academic Publishers, Boston.
  4. Fang Jinming, I-fuzzy Alexandrov topologies and specialization orders, Fuzzy Sets and Systems, 158 (2007), 2359-2374. https://doi.org/10.1016/j.fss.2007.05.001
  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.
  6. H. Lai and D. Zhang, Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems 157 (2006),1865-1885. https://doi.org/10.1016/j.fss.2006.02.013
  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. https://doi.org/10.1016/j.ijar.2008.12.002
  8. Z. Pawlak, Rough sets, Int. J. Comput. Inf. Sci. 11 (1982), 341-356. https://doi.org/10.1007/BF01001956
  9. Z. Pawlak, Rough probability, Bull. Pol. Acad. Sci. Math. 32 (1984), 607-615.
  10. A. M. Radzikowska and E.E. Kerre, A comparative study of fuzy rough sets, Fuzzy Sets and Systems 126 (2002), 137-155. https://doi.org/10.1016/S0165-0114(01)00032-X
  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. https://doi.org/10.1016/j.camwa.2009.03.100
  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. https://doi.org/10.1016/j.ins.2012.06.029

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