International Journal of Fuzzy Logic and Intelligent Systems

  • 제10권2호
  • /
  • Pages.152-156
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  • 2010
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  • 1598-2645(pISSN)
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  • 2093-744X(eISSN)
한국지능시스템학회 (Korean Institute of Intelligent Systems)
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Some Properties on Intuitionistic Fuzzy Metric Space

  • Park, Jong-Seo (Department of Mathematic Education, Chinju National University of Education) ;
  • Kwun, Young-Chel (Department of Mathematics, Dong-A University) ;
  • Park, Jin-Han (Division of Mathematical Sciences, Pukyong National University)
  • 투고 : 2009.11.08
  • 심사 : 2010.04.28
  • 발행 : 2010.06.25
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초록

We define some terminologies on intuitionistic fuzzy metric space and prove that the topology generated by any intuitionistic fuzzy metric space is metrizable. Also, we show that if the intuitionistic fuzzy metric space is complete, then the generated topology is completely metrizable, a Baire space, and that an intuitionistic fuzzy metric space is precompact if and only if every sequence has a Cauchy subsequence.

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참고문헌

  1. J., Dugundji, Topology, Korea; Top Publ., 1982.
  2. V., Gregori, S., Romaguera, "Some properties of fuzzy metric spaces", Fuzzy Sets and Systems, vol. 115 , pp. 485-489, 2000. https://doi.org/10.1016/S0165-0114(98)00281-4
  3. A., George, P., Veeramani, "On some results in fuzzy metric spaces", Fuzzy Sets and Systems, vol. 64, pp. 395-399, 1994. https://doi.org/10.1016/0165-0114(94)90162-7
  4. A., George, P., Veeramani, "On some results of analysis for fuzzy metric spaces", Fuzzy Sets and Systems, vol. 90, pp. 365-368, 1997. https://doi.org/10.1016/S0165-0114(96)00207-2
  5. J.L., Kelly, General topology, Van Nostrand, 1955.
  6. J., Kramosil, J., Michalek, "Fuzzy metric and statistical metric spaces", Kybernetica, vol. 11, pp. 326-334, 1975.
  7. J.H., Park, "Intuitionistic fuzzy metric spaces", Chaos Solitons & Fractals, vol. 22, no. 5, pp. 1039-1046, 2004. https://doi.org/10.1016/j.chaos.2004.02.051
  8. J.H., Park, J.S., Park, Y.C., Kwun, "A common fixed point theorem in the intuitionistic fuzzy metric space", Advances in Natural Comput. Data Mining(Proc. 2nd ICNC and 3rd FSKD), pp. 293-300, 2006.
  9. J.H., Park, J.S., Park, Y.C., Kwun, "Fixed point theorems in intuitionistic fuzzy metric space(I)", JP J. fixed point Theory & Appl. vol. 2, no. 1, pp. 79-89, 2007.
  10. J.S., Park, "On some results in intuitionistic fuzzy metric space", JP J. Fixed Point Theory & Appl. vol. 3, no. 1, pp. 39-48, 2008.
  11. J.S., Park, S.Y., Kim, "A fixed point theorem in a fuzzy metric space", F.J.M.S. vol. 1, no. 6, pp. 927-934, 1999.
  12. J.S., Park, S.Y., Kim, "Common fixed point theorem and example in intuitionistic fuzzy metric space", J. KIIS. vo. 18, no. 4, pp. 524-529, 2008. https://doi.org/10.5391/JKIIS.2008.18.4.524
  13. J.S., Park, Y.C., Kwun, "Some fixed point theorems in the intuitionistic fuzzy metric spaces", F.J.M.S. vol. 24, no. 2, pp. 227-239, 2007.
  14. J.S., Park, Y.C., Kwun, J.H., Park, "A fixed point theorem in the intuitionistic fuzzy metric spaces", F.J.M.S. vol. 16, no. 2, pp. 137-149, 2005.
  15. B., Schweizer, A., Sklar, "Statistical metric spaces", Pacific J. Math. vol. 10, pp. 314-334, 1960.