A theoretical approach on intuitionistic Fuzzy Hausdorff space

• Sivaraman, Geetha ; V. J., Jasmy ^[1]
  1. [1] Bharathidasan University

     Bharathidasan University

     India

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 42, Nº. 2, 2023, págs. 319-338
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-5409
• Enlaces
  • Texto completo
• Resumen

  • The object of this paper is to introduce a new definition for intuitionistic fuzzy Hausdorff space (IFHS). We investigate some of its characterizations and discuss it with some necessary counter examples. In addition, we compared the new notion with the existing notions. Finally we point out the significance of Hausdorffness in digital image processing.

• Referencias bibliográficas
  • K. T. Atanassov, “Intuitionistic fuzzy sets”, Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87-96, 1986. https://doi.org/10.1016/S0165-0114(86)80034-3
  • Md. Aman Mahbub, Md. Sahadat Hossain and M. Altab Hossain, “Separation Axioms in Intuitionistic Fuzzy Compact Topological Spaces”, Journal...
  • S. Bayhan and D. Coker, “On fuzzy separation axioms in intuitionistic fuzzy topological space”, Busefal, vol. 67, pp. 77-87, 1996.
  • C. L. Chang, “Fuzzy Topological Spaces”, Journal of Mathematical Analysis and Applications, vol. 24, pp. 182-190, 1968. https://doi.org/10.1016/0022-247X(68)90057-7
  • D. Coker, “An Introduction to intuitionistic fuzzy topological space”, Fuzzy Sets and Systems, vol. 88, no. 1, pp. 81-89, 1997. https://doi.org/10.1016/S0165-0114(96)00076-0
  • D. Coker and M. Demirci, “On intuitionistic fuzzy points”, Notes on Intuitionistic Fuzzy Sets, vol. 1, no. 2, pp. 79-84, 1995.
  • E. Ahmed, M.S. Hossain, and D.M. Ali, “On Intuitionistic Fuzzy T2 Spaces”, Journal of Bangladesh Academy of Sciences, vol. 10, no. 6, pp....
  • M. S. Islam, M. S. Hossain and M. Asaduzzaman, “Level separation on Intuitionistic fuzzy T2 spaces”, Journal of Mathematical and Computational...
  • S. J. Lee and E. P. Lee, “The category of intuitionistic fuzzy topological space”, Bulletin of the Korean Mathematical Society, vol. 37, pp....
  • R. Lowen, “Fuzzy Topological Spaces and Fuzzy compactness”, Journal of Mathematical Analysis and Applications, vol. 56, pp. 621-633, 1976....
  • F. G. Lupianez, “Hausdorffness in intuitionistic fuzzy topological space”, Mathware and Soft Computing, vol. 10, pp. 17-22, 2003.
  • Naimpally, A. Somashekhar, and F. James Peters. Topology with applications: topological spaces via near and far. World Scientific, 2013.
  • V. L. G. Nayagam and K. S. Murali, “IFT2 Spaces”, Journal of Combinatorics, Information System Sciences, vol. 33, pp. 141-149, 2008.
  • P. V. Ramakrishnan and V. L. G. Nayagam, “Nearly Fuzzy Hausdorff Spaces”, Indian Journal of Pure and Applied Mathematics, vol. 31, pp. 695-712,...
  • A. K. Singh and R. Srivastava, “Separation axioms in intuitionistic fuzzy topological spaces”, Advance in fuzzy systems, 2012. https://doi.org/10.1155/2012/604396
  • L. A. Zadeh, “Fuzzy sets”, Information and Control, vol. 8, no. 3, pp. 338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X