Intuitionistic Fuzzy Rough Approximation Operators

DOI QR코드

DOI QR Code

Yun, Sang Min;Lee, Seok Jong

  • 투고 : 2015.07.03
  • 심사 : 2015.09.24
  • 발행 : 2015.09.25

초록

Since upper and lower approximations could be induced from the rough set structures, rough sets are considered as approximations. The concept of fuzzy rough sets was proposed by replacing crisp binary relations with fuzzy relations by Dubois and Prade. In this paper, we introduce and investigate some properties of intuitionistic fuzzy rough approximation operators and intuitionistic fuzzy relations by means of topology.

키워드

Intuitionistic fuzzy topology;Intuitionistic fuzzy approximation space

참고문헌

  1. W. Tang, J. Wu, and D. Zheng, “On fuzzy rough sets and their topological structures,” Mathematical Problems in Engineering, vol. 2014, pp. 1–17, 2014.
  2. H. Bustince and P. Burillo, “Structures on intuitionistic fuzzy relations,” Fuzzy Sets and Systems, vol. 78, no. 3, pp. 293–303, 1996. https://doi.org/10.1016/0165-0114(96)84610-0
  3. L. Zhou, W.-Z. Wu, and W.-X. Zhang, “On intuitionistic fuzzy rough sets and their topological structures,” Int. J. Gen. Syst., vol. 38, no. 6, pp. 589–616, 2009. https://doi.org/10.1080/03081070802187723
  4. S. J. Lee and S. M. Yun, “Intuitionistic fuzzy topology and intuitionistic fuzzy preorder,” International Journal of Fuzzy Logic and Intelligent Systems, vol. 15, no. 1, pp. 79–86, 2015. https://doi.org/10.5391/IJFIS.2015.15.1.79
  5. K. Bageerathi, “A generalization of some open sets in intuitionistic fuzzy topological spaces,” Bull. Kerala Math. Assoc., vol. 11, no. 2, pp. 137–147, 2014.
  6. Z. Pawlak, “Rough sets,” Internat. J. Comput. Inform. Sci., vol. 11, no. 5, pp. 341–356, 1982. https://doi.org/10.1007/BF01001956
  7. D. Dubois and H. Prade, “Rogh fuzzy sets and fuzzy rough sets,” Int. J. Gen. Syst., vol. 17, pp. 191–209, 1990. https://doi.org/10.1080/03081079008935107
  8. H. Lai and D. Zhang, “Fuzzy preorder and fuzzy topology,” Fuzzy Sets and Systems, vol. 157, no. 14, pp. 1865–1885, 2006. https://doi.org/10.1016/j.fss.2006.02.013
  9. Z. M. Ma and B. Q. Hu, “Topological and lattice structures of l-fuzzy rough sets determined by lower and upper sets,” Inform. Sci., vol. 218, pp. 194–204, 2013. https://doi.org/10.1016/j.ins.2012.06.029
  10. Y. C. Kim, “Join-meet approximation operators induced by Alexandrov fuzzy topologies,” The Korean Journal of Mathematics, vol. 22, no. 3, pp. 553–565, 2014. https://doi.org/10.11568/kjm.2014.22.3.553
  11. E. Szmidt and J. Kacprzyk, “Distances between intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 114, no. 3, pp. 505–518, 2000. https://doi.org/10.1016/S0165-0114(98)00244-9
  12. L. Zhou and W.-Z. Wu, “On intuitionistic fuzzy topologies based on intuitionistic fuzzy reflexive and transitive relations,” Soft Computing, no. 15, pp. 1183–1194, 2011.
  13. R. Lowen, “Fuzzy topological spaces and fuzzy compactness,” J. Math. Anal. Appl., vol. 56, pp. 621–633, 1976. https://doi.org/10.1016/0022-247X(76)90029-9
  14. P. T. Johnstone, Stone Spaces. Cambridge: Cambridge University Press, 1982.
  15. C. L. Chang, “Fuzzy topological spaces,” J. Math. Anal. Appl., vol. 24, pp. 182–190, 1968. https://doi.org/10.1016/0022-247X(68)90057-7
  16. D. Coker, “An introduction to intuitionistic fuzzy topological spaces,” Fuzzy Sets and Systems, vol. 88, pp. 81–89, 1997. https://doi.org/10.1016/S0165-0114(96)00076-0
  17. K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, pp. 87–96, 1986. https://doi.org/10.1016/S0165-0114(86)80034-3
  18. D. Coker and M. Demirci, “An introduction to intuitionistic fuzzy topological spaces in Sostak’s sense,” BUSEFAL, vol. 67, pp. 67–76, 1996.
  19. S. J. Lee and E. P. Lee, “The category of intuitionistic fuzzy topological spaces,” Bull. Korean Math. Soc., vol. 37, no. 1, pp. 63–76, 2000.
  20. S. J. Lee and Y. S. Eoum, “Intuitionistic fuzzy 𝜃-closure and 𝜃-interior,” Commun. Korean Math. Soc., vol. 25, no. 2, pp. 273–282, 2010. https://doi.org/10.4134/CKMS.2010.25.2.273
  21. R. K. Thumbakara, “Intuitionistic fuzzy topological spaces and frames,” J. Fuzzy Math., vol. 18, no. 3, pp. 751–756, 2010.
  22. K. K. Azad and S. Mittal, “On Hausdorffness and compactness in intuitionistic fuzzy topological spaces,” Mat. Vesnik, vol. 63, no. 2, pp. 145–155, 2011.