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A note on intuitionistic fuzzy metric spaces

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  • Gregori, V.
  • Romaguera, S.
  • Veeramani, P.

Abstract

Recently, J.H. Park [J.H. Park, Intuitionistic fuzzy metric spaces. Chaos, Solitons & Fractals 2004;22:1039–46] introduced and studied a notion of intuitionistic fuzzy metric space by using the idea of intuitionistic fuzzy set due to Atanassov. In this note we show that for each intuitionistic fuzzy metric space (X,M,N,∗,♢), the topology generated by the intuitionistic fuzzy metric (M,N) coincides with the topology generated by the fuzzy metric M, and hence, the study of the space (X,M,N,∗,♢) reduces to the study of the fuzzy metric space (X,M,∗); so that, Park’s results follow directly from well-known theorems in fuzzy metric spaces.

Suggested Citation

  • Gregori, V. & Romaguera, S. & Veeramani, P., 2006. "A note on intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 902-905.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:4:p:902-905
    DOI: 10.1016/j.chaos.2005.08.113
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    References listed on IDEAS

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    1. El Naschie, M.S., 2005. "‘t Hooft ultimate building blocks and space–time as an infinite dimensional set of transfinite discrete points," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 521-524.
    2. El Naschie, M.S., 2005. "The two-slit experiment as the foundation of E-infinity of high energy physics," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 509-514.
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    Cited by:

    1. Sharma, Sushil & Deshpande, Bhavana, 2009. "Common fixed point theorems for finite number of mappings without continuity and compatibility on intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2242-2256.
    2. Hsien-Chung Wu, 2018. "Fuzzy Semi-Metric Spaces," Mathematics, MDPI, vol. 6(7), pages 1-19, June.
    3. Lael, Fatemeh & Nourouzi, Kourosh, 2008. "Some results on the IF-normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 931-939.
    4. Valentín Gregori & Juan-José Miñana & Bernardino Roig & Almanzor Sapena, 2020. "A Characterization of Strong Completeness in Fuzzy Metric Spaces," Mathematics, MDPI, vol. 8(6), pages 1-11, May.
    5. Hsien-Chung Wu, 2018. "Convergence in Fuzzy Semi-Metric Spaces," Mathematics, MDPI, vol. 6(9), pages 1-39, September.
    6. Saadati, R. & Sedghi, S. & Shobe, N., 2008. "Modified intuitionistic fuzzy metric spaces and some fixed point theorems," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 36-47.
    7. Goudarzi, M. & Vaezpour, S.M. & Saadati, R., 2009. "On the intuitionistic fuzzy inner product spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1105-1112.
    8. Miheţ, Dorel, 2009. "Fixed point theorems in probabilistic metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1014-1019.
    9. Miheţ, Dorel, 2009. "A note on a fixed point theorem in Menger probabilistic quasi-metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2349-2352.
    10. Saleem, Naeem & Ahmad, Khaleel & Ishtiaq, Umar & De la Sen, Manuel, 2023. "Multivalued neutrosophic fractals and Hutchinson-Barnsley operator in neutrosophic metric space," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    11. Saadati, Reza, 2008. "On the L-fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1419-1426.
    12. Deshpande, Bhavana, 2009. "Fixed point and (DS)-weak commutativity condition in intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2722-2728.
    13. Deschrijver, Glad & O’Regan, Donal & Saadati, Reza & Mansour Vaezpour, S., 2009. "L-Fuzzy Euclidean normed spaces and compactness," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 40-45.
    14. Saadati, Reza, 2009. "A note on “Some results on the IF-normed spaces”," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 206-213.
    15. Ješić, Siniša N., 2009. "Convex structure, normal structure and a fixed point theorem in intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 292-301.

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