Browse > Article
http://dx.doi.org/10.5391/IJFIS.2015.15.1.79

Intuitionistic Fuzzy Topology and Intuitionistic Fuzzy Preorder  

Yun, Sang Min (Department of Mathematics, Chungbuk National University)
Lee, Seok Jong (Department of Mathematics, Chungbuk National University)
Publication Information
International Journal of Fuzzy Logic and Intelligent Systems / v.15, no.1, 2015 , pp. 79-86 More about this Journal
Abstract
This paper is devoted to finding relationship between intuitionistic fuzzy preorders and intuitionistic fuzzy topologies. For any intuitionistic fuzzy preordered space, an intuitionistic fuzzy topology will be constructed. Conversely, for any intuitionistic fuzzy topological space, we obtain an intuitionistic fuzzy preorder on the set. Moreover, we will show that the family of all intuitionistic fuzzy preorders on an underlying set has a very close link to the family of all intuitionistic fuzzy topologies on the set satisfying some extra condition.
Keywords
Intuitionistic fuzzy topology; Intuitionistic fuzzy preorder;
Citations & Related Records
연도 인용수 순위
  • Reference
1 J. Kortelainen, "On relationship between modified sets, topological spaces and rough sets," Fuzzy Sets and Systems, vol. 61, no. 1, pp. 91-95, 1994. http://dx.doi.org/10.1016/0165-0114(94)90288-7   DOI   ScienceOn
2 Y. Y. Yao, "Two views of the theory of rough sets in finite universes," International Journal of Approximate Reasoning, vol. 15, no. 4, pp. 291-317, 1996. http://dx.doi.org/10.1016/S0888-613X(96)00071-0   DOI   ScienceOn
3 K. Qin and Z. Pei, "On the topological properties of fuzzy rough sets," Fuzzy Sets and Systems, vol. 151, no. 3, pp. 601-613, 2005. http://dx.doi.org/10.1016/j.fss.2004.08.017   DOI   ScienceOn
4 D. Dubois and H. Prade, "Rough fuzzy sets and fuzzy rough sets," International Journal of General System, vol. 17, no. 2-3, pp. 191-209, 1990. http://dx.doi.org/10.1080/03081079008935107   DOI   ScienceOn
5 N. N. Morsi and M. M. Yakout, "Axiomatics for fuzzy rough sets," Fuzzy Sets and Systems, vol. 100, no. 1-3, pp. 327-342, 1998. http://dx.doi.org/10.1016/S0165-0114(97)00104-8   DOI   ScienceOn
6 W. Z. Wu, J. S. Mi, and W. X. Zhang, "Generalized fuzzy rough sets," Information Sciences, vol. 151, pp. 263-282, 2003. http://dx.doi.org/10.1016/S0020-0255(02)00379-1   DOI   ScienceOn
7 S. P. Tiwari and A. K. Srivastava, "Fuzzy rough sets, fuzzy preorders and fuzzy topologies," Fuzzy Sets and Systems, vol. 210, pp. 63-68, 2013. http://dx.doi.org/10.1016/j.fss.2012.06.001   DOI   ScienceOn
8 K. T. Atanassov, "Intuitionistic fuzzy sets," Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87-96, 1986. http://dx.doi.org/10.1016/S0165-0114(86)80034-3   DOI   ScienceOn
9 E. Szmidt and J. Kacprzyk, "Distances between intuitionistic fuzzy sets," Fuzzy Sets and Systems, vol. 114, no. 3, pp. 505-518, 2000. http://dx.doi.org/10.1016/S0165-0114(98)00244-9   DOI   ScienceOn
10 H. Bustince and P. Burillo, "Structures on intuitionistic fuzzy relations," Fuzzy Sets and Systems, vol. 78, no. 3, pp. 293-303, 1996. http://dx.doi.org/10.1016/0165-0114(96)84610-0   DOI   ScienceOn
11 L. Zhou, W. Z. Wu, and W. X. Zhang, "On intuitionistic fuzzy rough sets and their topological structures," International Journal of General Systems, vol. 38, no. 6, pp. 589-616, 2009. http://dx.doi.org/10.1080/03081070802187723   DOI   ScienceOn
12 W. Z. Wu and L. Zhou, "On intuitionistic fuzzy topologies based on intuitionistic fuzzy reflexive and transitive relations," Soft Computing, vol. 15, no. 6, pp. 1183-1194, 2011. http://dx.doi.org/10.1007/s00500-010-0576-0   DOI
13 D. Coker, "An introduction to intuitionistic fuzzy topological spaces," Fuzzy Sets and Systems, vol. 88, no. 1, pp. 81-89, 1997. http://dx.doi.org/10.1016/S0165-0114(96)00076-0   DOI   ScienceOn
14 R. Lowen, "Fuzzy topological spaces and fuzzy compactness," Journal of Mathematical Analysis and Applications, vol. 56, no. 3, pp. 621-633, 1976. http://dx.doi.org/10.1016/0022-247X(76)90029-9   DOI
15 M. Mas, M. Monserrat, J. Torrens, and E. Trillas, "A survey on fuzzy implication functions," IEEE Transactions on Fuzzy Systems, vol. 15, no. 6, pp. 1107-1121, 2007. http://dx.doi.org/10.1109/TFUZZ.2007.896304   DOI   ScienceOn
16 B. De Baets and J. Fodor, "Residual operators of uninorms," Soft Computing, vol. 3, no. 2, pp. 89-100, 1999. http://dx.doi.org/10.1007/s005000050057   DOI
17 P. T. Johnstone, Stone Spaces. Cambridge: Cambridge University Press, 1982.
18 Z. Pawlak, "Rough sets," International Journal of Computer & Information Sciences, vol. 11, no. 5, pp. 341-356, 1982. http://dx.doi.org/10.1007/BF01001956   DOI