Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON FUZZY BITOPOLOGICAL SPACES IN ŠOSTAK'S SENSE (II)

  • Received : 2006.06.08
  • Published : 2010.07.31
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Abstract

In this paper, we have use a fuzzy bitopological space (X, $\tau_1$, $\tau_2$) to create a family $\tau_{ij}^s$ which is a supra fuzzy topology on X. Also, we introduce and study the concepts of r-($\tau_i$, $\tau_j$)-generalized fuzzy regular closed, r-($\tau_i$, $\tau_j$)-generalized fuzzy strongly semi-closed and r-($\tau_i$, $\tau_j$)-generalized fuzzy regular strongly semi-closed sets in fuzzy bitopological space in the sense of $\check{S}$ostak. Also, these classes of fuzzy subsets are applied for constructing several type of fuzzy closed mapping and some type of fuzzy separation axioms called fuzzy binormal, fuzzy mildly binormal and fuzzy almost pairwise normal.

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References

  1. S. E. Abbas, A study of smooth topological spaces, Ph. D. Thesis, South Valley University,2002.
  2. C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968), 182–190. https://doi.org/10.1016/0022-247X(68)90057-7
  3. K. C. Chattopadhyay, R. N. Hazra, and S. K. Samanta, Gradation of openness: fuzzytopology, Fuzzy Sets and Systems 49 (1992), no. 2, 237–242. https://doi.org/10.1016/0165-0114(92)90329-3
  4. K. C. Chattopadhyay and S. K. Samanta, Fuzzy topology: fuzzy closure operator, fuzzycompactness and fuzzy connectedness, Fuzzy Sets and Systems 54 (1993), no. 2, 207–212. https://doi.org/10.1016/0165-0114(93)90277-O
  5. M. K. El Gayyar, E. E. Kerre, and A. A. Ramadan, Almost compactness and nearcompactness in smooth topological spaces, Fuzzy Sets and Systems 62 (1994), no. 2,193–202. https://doi.org/10.1016/0165-0114(94)90059-0
  6. M. H. Ghanim, O. A. Tantawy, and F. M. Selim, Gradation of supra-openness, FuzzySets and Systems 109 (2000), no. 2, 245–250. https://doi.org/10.1016/S0165-0114(97)00342-4
  7. U. Hohle and A. P. Sostak, A general theory of fuzzy topological spaces, Fuzzy topology.Fuzzy Sets and Systems 73 (1995), no. 1, 131–149. https://doi.org/10.1016/0165-0114(94)00368-H
  8. Y. C. Kim, r-fuzzy semi-open sets in fuzzy bitopological spaces, Far East J. Math. Sci.(FJMS) Special Volume (2000), Part II, 221–236.
  9. Y. C. Kim, ${\delta}-closure$ operators in fuzzy bitopological spaces, Far East J. Math. Sci. (FJMS)2 (2000), no. 5, 791–808.
  10. Y. C. Kim, A. A. Ramadan, and S. E. Abbas, Some weakly forms of fuzzy continuousmappings in L-fuzzy bitopological spaces, J. Fuzzy Math. 9 (2001), no. 2, 483–495.
  11. Y. C. Kim, A. A. Ramadan, and S. E. Abbas, Separation axioms in terms of ${\theta}-closure\;and\;{\delta}-closure$ operators, Indian J. PureAppl. Math. 34 (2003), no. 7, 1067–1083.
  12. T. Kubiak and A. P. Sostak, Lower set-valued fuzzy topologies, Quaestiones Math. 20(1997), no. 3, 423–429. https://doi.org/10.1080/16073606.1997.9632016
  13. E. P. Lee, Preopen sets in smooth bitopological spaces, Commun. Korean Math. Soc. 18(2003), no. 3, 521–532. https://doi.org/10.4134/CKMS.2003.18.3.521
  14. P. M. Pu and Y. M. Liu, Fuzzy topology. I. Neighborhood structure of a fuzzy point andMoore-Smith convergence, J. Math. Anal. Appl. 76 (1980), no. 2, 571–599. https://doi.org/10.1016/0022-247X(80)90048-7
  15. A. A. Ramadan, Smooth topological spaces, Fuzzy Sets and Systems 48 (1992), no. 3,371–375. https://doi.org/10.1016/0165-0114(92)90352-5
  16. A. A. Ramadan and S. E. Abbas, On several types of continuity in fuzzy bitopologicalspaces, J. Fuzzy Math. 9 (2001), no. 2, 399–412.
  17. A. A. Ramadan, S. E. Abbas, and A. A. Abd El-latif, On fuzzy bitopological spaces inSostak’s sense, Commun. Korean Math. Soc. 21 (2006), no. 3, 497–514. https://doi.org/10.4134/CKMS.2006.21.3.497
  18. A. P. Sostak, On a fuzzy topological structure, Rend. Circ. Mat. Palermo (2) Suppl. No.11 (1985), 89–103.
  19. A. P. Sostak, On the neighborhood structure of fuzzy topological spaces, Zb. Rad. No. 4 (1990),7–14.
  20. A. P. Sostak, Basic structures of fuzzy topology, J. Math. Sci. 78 (1996), no. 6, 662–701. https://doi.org/10.1007/BF02363065