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Fuzzy β-(r, s)-Open Sets in Smooth Bitopological Spaces

  • Lee, Seung-On (Department of Mathematics, Chungbuk National University) ;
  • Lee, Eun-Pyo (Department of Mathematics, Seonam University)
  • Received : 2010.01.04
  • Accepted : 2010.03.15
  • Published : 2010.06.25

Abstract

We introduce and investigate the concepts of ($T_i,T_j$)-fuzzy $\beta$-(r, s)-open sets, ($T_i,T_j$)-fuzzy $\beta$-(r, s)-closed sets and fuzzy pairwise $\beta$-(r, s)-continuous mappings in smooth bitopological spaces.

Keywords

References

  1. K. K. Azad, ”On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity,” J. Math. Anal. Appl., vol. 82, pp. 14-32, 1981. https://doi.org/10.1016/0022-247X(81)90222-5
  2. 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
  3. K. C. Chattopadhyay, R. N. Hazra, and S. K. Samanta, ”Gradation of openness : Fuzzy topology,” Fuzzy Sets and Systems, vol. 49, 237-242, 1992. https://doi.org/10.1016/0165-0114(92)90329-3
  4. A. Kandil, ”Biproximities and fuzzy bitopological spaces,” Simon Stevin, vol. 63, pp. 45-66. 1989.
  5. E. P. Lee, ”Pairwise semicontinuous mappings in smooth bitopological spaces,” Journal of Fuzzy Logic and Intelligent Systems, vol. 12, pp. 268-274, 2002.
  6. E. P. Lee, ”Preopen sets in smooth bitopological spaces,” Commun. Korean Math. Soc., vol. 18, pp. 521-532, 2003. https://doi.org/10.4134/CKMS.2003.18.3.521
  7. S. O. Lee and E. P. Lee, ”Fuzzy strongly (r, s)-semiopen sets,” International J. Fuzzy Logic and Intelligent Systems, vol. 6, pp. 299-303, 2006. https://doi.org/10.5391/IJFIS.2006.6.4.299
  8. J. H. Park and B. Y. Lee, ”Fuzzy semi-preopen sets and fuzzy semi-precontinuous mappings,” Fuzzy Sets and Systems, vol. 67, pp. 359-364, 1994. https://doi.org/10.1016/0165-0114(94)90264-X
  9. A. A. Ramadan, ”Smooth topological spaces”, Fuzzy Sets and Systems, vol. 48, pp. 371-375, 1992. https://doi.org/10.1016/0165-0114(92)90352-5
  10. S. Sampath Kumar, ”Semi-open sets, semi-continuity and semi-open mappings in fuzzy bitopological spaces,” Fuzzy Sets and Systems, vol. 64, pp. 421-426, 1994. https://doi.org/10.1016/0165-0114(94)90166-X
  11. A. P. Sostak, ”On a fuzzy topological structure,” Suppl. Rend. Circ. Matem. Janos Palermo, Sr. II, vol. 11, pp. 89-103, 1985.
  12. L. A. Zadeh, ”Fuzzy sets,” Information and Control, vol. 8, pp. 338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X