International Journal of Fuzzy Logic and Intelligent Systems

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Rough Approximations on Preordered Sets

  • Kim, Yong-Chan (Department of Mathematics, Gangneung-Wonju National University) ;
  • Kim, Young-Sun (Department of Applied Mathematics, Pai Chai University)
  • Received : 2011.10.30
  • Accepted : 2011.12.02
  • Published : 2011.12.25
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Abstract

In this paper, we investigate the properties of rough approximations defined by preordered sets. We study the relations among the lower and upper rough approximations, closure and interior systems, and closure and interior operators.

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References

  1. R. Belohlavek, "Lattices of fixed points of Galois connections," Math. Logic Quart., vol.47, pp.111-116, 2001. https://doi.org/10.1002/1521-3870(200101)47:1<111::AID-MALQ111>3.0.CO;2-A
  2. G. Georgescu, A. Popescue, "Non-dual fuzzy connections," Arch. Math. Log., vol. 43, pp.1009-1039, 2004. https://doi.org/10.1007/s00153-004-0240-4
  3. J. Jarvinen, M. Kondo, J. Kortelainen, "Logics from Galois connections," Int. J. Approx. Reasoning, vol.49, pp.595-606, 2008. https://doi.org/10.1016/j.ijar.2008.06.003
  4. Y.C. Kim, Y.S. Kim, "Relations and upper sets on partially ordered sets," Int. Math. Forum, vol. 6, no.19, pp.899-908, 2011.
  5. Y.C. Kim, Y.S. Kim, "Various connections on interior sets," Int. Math. Forum, vol.6, no.19, pp. 909-920, 2011.
  6. Z. Pawlak," Rough sets," Int. J. Comput. Inf. Sci., vol.11, pp.341-356, 1982. https://doi.org/10.1007/BF01001956
  7. G. Qi andW. Liu," Rough operations on Boolean algebras," Information Sciences, vol. 173, pp.49-63, 2005. https://doi.org/10.1016/j.ins.2004.06.006
  8. R. Wille, Restructuring lattice theory; an approach based on hierarchies of concept, in: 1. Rival(Ed.), Ordered Sets, Reidel, Dordrecht, Boston, 1982.