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Delta Closure and Delta Interior in Intuitionistic Fuzzy Topological Spaces

  • Eom, Yeon Seok (Department of Mathematics, Chungbuk National University) ;
  • Lee, Seok Jong (Department of Mathematics, Chungbuk National University)
  • Received : 2012.09.26
  • Accepted : 2012.12.18
  • Published : 2012.12.25

Abstract

Due to importance of the concepts of ${\theta}$-closure and ${\delta}$-closure, it is natural to try for their extensions to fuzzy topological spaces. So, Ganguly and Saha introduced and investigated the concept of fuzzy ${\delta}$-closure by using the concept of quasi-coincidence in fuzzy topological spaces. In this paper, we will introduce the concept of ${\delta}$-closure in intuitionistic fuzzy topological spaces, which is a generalization of the ${\delta}$-closure by Ganguly and Saha.

Keywords

References

  1. M. N. Mukherjee and S. P. Sinha, "Fuzzy $\theta$-closure operator on fuzzy topological spaces," Internat. J. Math. Math. Sci., vol. 14, no. 2, pp. 309-314, 1991. https://doi.org/10.1155/S0161171291000364
  2. N. V. Velicko, "H-closed topological spaces," Mat. Sb. (N.S.), vol. 70 (112), pp. 98-112, 1966.
  3. N. V. Velicko, "On the theory of H-closed topological spaces," Sibirsk. Mat. Z., vol. 8, pp. 754-763, 1967..
  4. R. F. Dickman, Jr. and J. R. Porter, "$\theta$-closed subsets of Hausdorff spaces," Pacific J. Math., vol. 59, no. 2, pp. 407-415, 1975. https://doi.org/10.2140/pjm.1975.59.407
  5. M. S. Espelie and J. E. Joseph, "Some properties of $\theta$-closure," Canad. J. Math., vol. 33, no. 1, pp. 142-149, 1981. [Online]. Available: http://dx.doi.org/10.4153/CJM-1981-013-8
  6. D. Sivaraj, "Semiopen set characterizations of almost-regular spaces," Glas. Mat. Ser. III, vol. 21(41), no. 2, pp. 437-440, 1986.
  7. S. Ganguly and S. Saha, "A note on $\delta$-continuity and $\delta$-connected sets in fuzzy set theory," Simon Stevin, vol. 62, pp. 127-141, 1988.
  8. I. M. Hanafy, A. M. Abd El-Aziz, and T. M. Salman, "Intuitionistic fuzzy $\theta$-closure operator," Bol. Asoc. Mat. Venez., vol. 13, no. 1, pp. 27-39, 2006.
  9. S. J. Lee and J. T. Kim, "Fuzzy strongly (r; s)-precontinuous mappings," IEEE International Conference on Fuzzy Systems, vol. 2009, pp. 581-586, 2009.
  10. S. J. Lee and J. T. Kim, "fuzzy strongly (r,s)-pre-open and preclosed mappings," Commun. Korean Math. Soc., vol. 26, no. 4, pp. 661-667, 2011. https://doi.org/10.4134/CKMS.2011.26.4.661
  11. S. J. Lee and S. M. Yun, "Fuzzy delta separation axioms," IEEE International Conference on Fuzzy Systems, vol. 2011, pp. 592-602, 2011.
  12. S. J. Lee and J. T. Kim, "Properties of fuzzy (r; s)-semi-irresolute mappings in intuitionistic fuzzy topological spaces," International Journal of Fuzzy Logic and Intelligent Systems, vol. 11, no. 3, pp. 190-196, 2011. https://doi.org/10.5391/IJFIS.2011.11.3.190
  13. K. T. Atanassov, "Intuitionistic fuzzy sets," vol. 20, pp. 87-96, 1986.
  14. 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
  15. D. Coker, "An introduction to fuzzy subspaces in intuitionistic fuzzy topological spaces," J. Fuzzy Math., vol. 4, no. 4, pp. 749-764, 1996.
  16. D. Coker and M. Demirci, "On intuitionistic fuzzy points," Notes IFS, vol. 1, no. 2, pp. 79-84, 1995.
  17. I. M. Hanafy, "Intuitionistic fuzzy functions," International Journal of Fuzzy Logic and Intelligent Systems, vol. 3, pp. 200-205, 2003. https://doi.org/10.5391/IJFIS.2003.3.2.200
  18. H. Gurcay, D. Coker, and A. H. Es, "On fuzzy continuity in intuitionistic fuzzy topological spaces," J. Fuzzy Math., vol. 5, pp. 365-378, 1997.