DOI QR코드

DOI QR Code

ON INTUITIONISTIC FUZZY SUBSPACES

  • Ramadan, Ahmed Abd El-Kader ;
  • El-Latif, Ahmed Aref Abd
  • Published : 2009.07.31

Abstract

We introduce a new concept of intuitionistic fuzzy topological subspace, which coincides with the usual concept of intuitionistic fuzzy topological subspace due to Samanta and Mondal [18] in the case that $\mu=X_A$ for A $\subseteq$ X. Also, we introduce and study some concepts such as continuity, separation axioms, compactness and connectedness in this sense.

Keywords

intuitionistic fuzzy subspace;intuitionistic fuzzy $\mu$ (continuity, separation axioms, compactness and connectedness)

References

  1. K. Atanassov, Intuitionistic fuzzy sets, VII ITKR's Session, Sofia (September, 1983) (in Bularian)
  2. K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), no. 1, 87–96 https://doi.org/10.1016/S0165-0114(86)80034-3
  3. K. Atanassov, New operators defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems 61 (1993), no. 2, 131–142 https://doi.org/10.1016/0165-0114(94)90229-1
  4. C. L. Chang, Fuzzy topological spaces, J. Math. Anall. Apll. 24 (1968), 182–190
  5. K. C. Chattopadhyay, R. N. Hazra, and S. K. Samanta, Gradation of openness: fuzzy topology, Fuzzy Sets and Systems 94 (1992), 237–242 https://doi.org/10.1016/0165-0114(92)90329-3
  6. D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems 88 (1997), 81–89 https://doi.org/10.1016/S0165-0114(96)00076-0
  7. D. Coker and A. H. Es, On fuzzy compactness in intuitionistic fuzzy topological spaces, J. Fuzzy Mathematics 3 (1995), no. 4, 899–909
  8. M. Demirci, Neighborhood structures in smooth topological spaces, Fuzzy Sets and Systems 92 (1997), 123–128 https://doi.org/10.1016/S0165-0114(96)00132-7
  9. Y. C. Kim, Initial L-fuzzy closure spaces, Fuzzy Sets and Systems 133 (2003), 277–297 https://doi.org/10.1016/S0165-0114(02)00224-5
  10. E. P. Lee and Y. B. Im, Mated fuzzy topological spaces, Int. Journal of Fuzzy Logic and Intelligent Systems 11 (2001), no. 2, 161–165
  11. W. K. Min and C. K. Park, Some results on intuitionistic fuzzy topological spaces defined by intuitionistic gradation of openness, Commun. Korean Math. Soc. 20 (2005), no. 4, 791–801 https://doi.org/10.4134/CKMS.2005.20.4.791
  12. P. M. Pu and Y. M. Liu, Fuzzy topology I: Neighborhood structure of a fuzzy point and Moor-Smith convergence, J. Math. Anal. Appl. 76 (1980), 571–599 https://doi.org/10.1016/0022-247X(80)90048-7
  13. A. A. Ramadan, Smooth topological spaces, Fuzzy Sets and Systems 48 (1992), 371–375 https://doi.org/10.1016/0165-0114(92)90352-5
  14. S. K. Samanta and T. K. Mondal. Intuitionistic gradation of openness: intuitionistic fuzzy topology, Busefal 73 (1997), 8–17
  15. A. P. Sostak, On a fuzzy topological structure, Supp. Rend. Circ. Math. Palermo (Ser.II) 11 (1985), 89–103
  16. A. P. Sostak, On the neighbourhood structure of a fuzzy topological space, Zb. Rodova Univ. Nis, ser Math. 4 (1990), 7–14
  17. A. P. Sostak, Basic structure of fuzzy topology, J. of Math. Sciences 78 (1996), no. 6, 662–701 https://doi.org/10.1007/BF02363065
  18. A. M. Zahran, On fuzzy subspaces, Kyungpook Math. J. 41 (2001), 361–369
  19. K. C. Chattopadhyay and S. K. Samanta, Fuzzy topology: fuzzy closure operator, fuzzy compactness and fuzzy connectedness, Fuzzy Sets and Systems 54 (1993), 207–212 https://doi.org/10.1016/0165-0114(93)90277-O
  20. U. Hohle and A. P. Sostak, A general theory of fuzzy topological spaces, Fuzzy Sets and Systems 73 (1995), 131–149 https://doi.org/10.1016/0165-0114(94)00368-H
  21. Y. C. Kim and S. E. Abbas, Connectedness in intuitionistic fuzzy topological spaces, Commun. Korean Math. Soc. 20 (2005), no. 1, 117–134 https://doi.org/10.4134/CKMS.2005.20.1.117
  22. S. K. Samanta and T. K. Mondal. On intuitionistic gradation of openness, Fuzzy Sets and Systems 31 (2002), 323–336 https://doi.org/10.1016/S0165-0114(01)00235-4