IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v28y2006i4p902-905.html
   My bibliography  Save this article

A note on intuitionistic fuzzy metric spaces

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905007216
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.08.113?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hsien-Chung Wu, 2018. "Fuzzy Semi-Metric Spaces," Mathematics, MDPI, vol. 6(7), pages 1-19, June.
    2. 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.
    3. 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.
    4. Miheţ, Dorel, 2009. "Fixed point theorems in probabilistic metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1014-1019.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Lael, Fatemeh & Nourouzi, Kourosh, 2008. "Some results on the IF-normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 931-939.
    10. 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.
    11. Hsien-Chung Wu, 2018. "Convergence in Fuzzy Semi-Metric Spaces," Mathematics, MDPI, vol. 6(9), pages 1-39, September.
    12. 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).
    13. Saadati, Reza, 2008. "On the L-fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1419-1426.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lael, Fatemeh & Nourouzi, Kourosh, 2008. "Some results on the IF-normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 931-939.
    2. Basu, C.K. & Mandal, S.S., 2009. "A note on disconnectedness," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3242-3246.
    3. El Naschie, M.S., 2006. "Elementary prerequisites for E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 579-605.
    4. El Naschie, M.S., 2005. "Stability Analysis of the two-slit experiment with quantum particles," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 291-294.
    5. Miheţ, Dorel, 2009. "Fixed point theorems in probabilistic metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1014-1019.
    6. 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.
    7. Zorlutuna, İdris, 2008. "On strong forms of completely irresolute functions," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 970-979.
    8. El Naschie, M.S., 2005. "From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 969-977.
    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. El Naschie, M.S., 2008. "High energy physics and the standard model from the exceptional Lie groups," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 1-17.
    11. El Naschie, M.S., 2005. "Non-Euclidean spacetime structure and the two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 1-6.
    12. Mukhamedov, Alfred M., 2007. "The two-slit gedanken experiment in E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 1-4.
    13. Caldas, Miguel & Jafari, Saeid, 2009. "A new decomposition of β-open functions," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 10-12.
    14. Materassi, Massimo & Wernik, Andrzej W. & Yordanova, Emiliya, 2006. "Statistics in the p-model," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 642-655.
    15. El Naschie, Mohamed Saladin, 2006. "The idealized quantum two-slit gedanken experiment revisited—Criticism and reinterpretation," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 843-849.
    16. Mukhamedov, A.M., 2007. "E-infinity as a fiber bundle and its thermodynamics," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 717-724.
    17. Ekici, Erdal, 2008. "On contra πg-continuous functions," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 71-81.
    18. Ekici, Erdal, 2007. "On almost πgp-continuous functions," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1935-1944.
    19. Al-Khawaja, Sameer, 2008. "Impulsive current-induced superconducting junction in spatially broken symmetry of fluxons," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 382-387.
    20. Azab Abd-Allah, M. & El-Saady, Kamal & Ghareeb, A., 2009. "(r,s)-Fuzzy F-open sets and (r,s)-fuzzy F-closed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 649-656.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:28:y:2006:i:4:p:902-905. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.