International Journal of Fuzzy Logic and Intelligent Systems

Korean Institute of Intelligent Systems (한국지능시스템학회)
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L-upper Approximation Operators and Join Preserving Maps

  • Kim, Yong Chan (Department of Mathematics, Gangneung-Wonju National University) ;
  • Kim, Young Sun (Department of Applied Mathematics, Pai Chai University)
  • Received : 2014.01.17
  • Accepted : 2014.09.22
  • Published : 2014.09.25
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Abstract

In this paper, we investigate the properties of join and meet preserving maps in complete residuated lattice using Zhang's the fuzzy complete lattice which is defined by join and meet on fuzzy posets. We define L-upper (resp. L-lower) approximation operators as a generalization of fuzzy rough sets in complete residuated lattices. Moreover, we investigate the relations between L-upper (resp. L-lower) approximation operators and L-fuzzy preorders. We study various L-fuzzy preorders on $L^X$. They are considered as an important mathematical tool for algebraic structure of fuzzy contexts.

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References

  1. Z. Pawlak, "Rough sets," International Journal of Computer & Information Sciences, vol. 11, no. 5, pp. 341-356, Oct. 1982. http://dx.doi.org/10.1007/BF01001956
  2. Z. Pawlak, "Rough probability," Bulletin of the Polish Academy of Sciences: Mathematics, vol. 32, pp. 607-615, 1984.
  3. P. H'ajek, Metamathematics of Fuzzy Logic, Dordrecht: Kluwer, 1998.
  4. R. Belohl'avek, Fuzzy Relational Systems: Foundations and Principles, New York, NY: Kluwer Academic/Plenum Publishers, 2002.
  5. A. M. Radzikowska and E. E. Kerre, "A comparative study of fuzzy rough sets," Fuzzy Sets and Systems, vol. 126, no. 2, pp. 137-155, Mar. 2002. http://dx.doi.org/10.1016/S0165-0114(01)00032-X
  6. Y. H. She and G. J. Wang, "An axiomatic approach of fuzzy rough sets based on residuated lattices," Computers & Mathematics with Applications, vol. 58, no. 1, pp. 189-201, Jul. 2009. http://dx.doi.org/10.1016/j.camwa.2009.03.100
  7. Q. Y. Zhang and L. Fan, "Continuity in quantitative domains," Fuzzy Sets and Systems, vol. 154, no. 1, pp. 118-131, Aug. 2005. http://dx.doi.org/10.1016/j.fss.2005.01.007
  8. Q. Zhang, W. Xie, and L. Fan, "Fuzzy complete lattices," Fuzzy Sets and Systems, vol. 160, no. 16, pp. 2275-2291, Aug. 2009. http://dx.doi.org/10.1016/j.fss.2008.12.001
  9. H. Lai and D. Zhang, "Fuzzy preorder and fuzzy topology," Fuzzy Sets and Systems, vol. 157, no. 14, pp. 1865-1885, Jul. 2006. http://dx.doi.org/10.1016/j.fss.2006.02.013
  10. H. Lai and D. Zhang, "Concept lattices of fuzzy contexts: formal concept analysis vs. rough set theory," International Journal of Approximate Reasoning, vol. 50, no. 5, pp. 695-707, May 2009. http://dx.doi.org/10.1016/j.ijar.2008.12.002
  11. Z.M. Ma and B. Q. Hu, "Topological and lattice structures of -fuzzy rough sets determined by lower and upper sets," Information Sciences, vol. 218, pp. 194-204, Jan. 2013. http://dx.doi.org/10.1016/j.ins.2012.06.029
  12. Y. C. Kim, "Alexandrov L-topologies and L-join meet approximatin operators," International Journal of Pure and Applied Mathematics, vol. 91, no. 1, pp. 113-129, 2014. http://dx.doi.org/10.12732/ijpam.v91i1.12