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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 854942, 8 pages
http://dx.doi.org/10.1155/2012/854942
Research Article

On Interval-Valued Supra-Fuzzy Syntopogenous Structure

Mathematics Department, Faculty of Science, Zagazig University, Zagazig 44519, Egypt

Received 12 August 2012; Accepted 1 November 2012

Academic Editor: Hamid Reza Karimi

Copyright © 2012 F. M. Sleim and Heba I. Mustafa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Csaszar, Foundations of General Topology, A Pergamon Press Book, Pergamon Press, New York, NY, USA, 1963. View at Zentralblatt MATH
  2. A. K. Katsaras, “On fuzzy syntopogenous structures,” Revue Roumaine de Mathématiques Pures et Appliquées, vol. 30, no. 6, pp. 419–431, 1985. View at Zentralblatt MATH
  3. M. Z. Wen, L. W. Jin, and S. Lan, “On fuzzy syntopogenous structures and preorder,” Fuzzy Sets and Systems, vol. 90, no. 3, pp. 355–359, 1997. View at Publisher · View at Google Scholar
  4. K. A. Hashem, “T-syntopogenous spaces,” Annals of Fuzzy Mathematics and Informatics, vol. 4, no. 1, pp. 25–48, 2012.
  5. C. L. Chang, “Fuzzy topological spaces,” Journal of Mathematical Analysis and Applications, vol. 24, pp. 182–190, 1968. View at Zentralblatt MATH
  6. B. Hutton, “Uniformities on fuzzy topological spaces,” Journal of Mathematical Analysis and Applications, vol. 58, no. 3, pp. 559–571, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. L. Wang-Jin, “Fuzzy proximity spaces redefined,” Fuzzy Sets and Systems, vol. 15, no. 3, pp. 241–248, 1985. View at Publisher · View at Google Scholar
  8. A. K. Katsaras, “Operations on fuzzy syntopogenous structures,” Fuzzy Sets and Systems, vol. 43, no. 2, pp. 199–217, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. R. Lowen, “Fuzzy topological spaces and fuzzy compactness,” Journal of Mathematical Analysis and Applications, vol. 56, no. 3, pp. 621–633, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. R. Lowen, “Fuzzy uniform spaces,” Journal of Mathematical Analysis and Applications, vol. 82, no. 2, pp. 370–385, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. G. Artico and R. Moresco, “Fuzzy proximities compatible with Lowen fuzzy uniformities,” Fuzzy Sets and Systems, vol. 21, no. 1, pp. 85–98, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. A. A. Ramadan, S. N. El-Deeb, M.-S. Saif, and M. El-Dardery, “Fuzzifying syntopogenous structures,” Journal of Fuzzy Mathematics, vol. 7, no. 3, pp. 535–546, 1999. View at Zentralblatt MATH
  13. M. S. Ying, “A new approach for fuzzy topology,” Fuzzy Sets and Systems, vol. 53, no. 1, pp. 93–104, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. A. Kandil, A. A. Nouh, and S. A. El-Sheikh, “On fuzzy bitopological spaces,” Fuzzy Sets and Systems, vol. 74, no. 3, pp. 353–363, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. M. H. Ghanim, O. A. Tantawy, and F. M. Salem, “On supra fuzzy syntopogenous space,” in Proceeding of the Conference on Geometry Topology and Application, Cairo University, December 1997.
  16. L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning. I,” Information Sciences, vol. 8, pp. 199–249, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. I. Grattan-Guiness, “Fuzzy membership mapped onto interval and many-valued quantities,” Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 22, pp. 149–160, 1975.
  18. K. U. Jahn, “Intervall-wertige Mengen,” Mathematische Nachrichten, vol. 68, pp. 115–132, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. R. Sambuc, Function Φ-flous, application a l’aide au diagnostic en pathologie thyroidienne [Ph.D. thesis], University of Marseille, Marseille, France, 1975.
  20. K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. D. Dubois, P. Hájek, and H. Prade, “Knowledge-driven versus data-driven logics,” Journal of Logic, Language and Information, vol. 9, no. 1, pp. 65–89, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338–353, 1965. View at Zentralblatt MATH
  23. J. Hongmei, “Multicriteria fuzzy decision-making methods based on interval-valued fuzzy sets,” in Proceedings of the 5th International Conference on Intelligent Computation Technology and Automation (ICICTA'12), pp. 217–220, Hunan, China, January 2012.
  24. J. Hong and F. Wang, “A similarity measure for interval-valued fuzzy sets and its application in supporting medical diagnostic reasoning,” in Proceedings of the 10th International Symposium on Operations Research and Its Applications (ISORA'11), pp. 251–257, Dunhuang, China, August 2011.
  25. H. Choi, G. Mun, J. Ahn, and C. Korea, “A medical diagnosis based on interval valued fuzzy set,” Biomedical Engineering: Applications, Basis and Communications, vol. 24, no. 4, p. 349, 2012. View at Publisher · View at Google Scholar
  26. F. M. Sleim, “On interval valued-supra-openness,” submitted for publication to the acta mathematica sinica journal.
  27. A. S. Mashhour, A. A. Allam, F. S. Mahmoud, and F. H. Khedr, “On supratopological spaces,” Indian Journal of Pure and Applied Mathematics, vol. 14, no. 4, pp. 502–510, 1983. View at Zentralblatt MATH
  28. A. E. Samuel and M. Balamurugan, “Fuzzy max-min composition technique in medical diagnosis,” Applied Mathematical Sciences, vol. 6, no. 35, pp. 1741–1746, 2012. View at Zentralblatt MATH
  29. Z. Pawlak, “Rough sets,” International Journal of Computer and Information Sciences, vol. 11, no. 5, pp. 341–356, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  30. A. S. Salama, “Some topological properties of rough sets with tools for data mining,” International Journal of Computer Science Issues, vol. 8, no. 3, part 2, pp. 1694–0814, 2011.
  31. R. Raghavan and B. K. Tripathy, “On some topological properties of multigranular rough sets,” Advances in Applied Science Research, vol. 2, no. 3, pp. 536–543, 2011.