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Fuzzy Extension of Crisp Metric by Means of Fuzzy Equivalence Relation

Author

Listed:
  • Olga Grigorenko

    (Institute of Mathematics and CS, University of Latvia, 1459 Riga, Latvia)

  • Alexander Šostak

    (Institute of Mathematics and CS, University of Latvia, 1459 Riga, Latvia
    Departments of Mathematics, University of Latvia, 1004 Riga, Latvia)

Abstract

We develop an alternative approach to the fuzzy metric concept, which we obtain by fuzzy extension of a crisp metric d on a set X by means of a fuzzy equivalence relation E on the set I R + . We call it an E - d metric and study its properties and relations with “classical” fuzzy metrics. Our special interest is in the topologies and fuzzy topologies induced by E - d metrics.

Suggested Citation

  • Olga Grigorenko & Alexander Šostak, 2022. "Fuzzy Extension of Crisp Metric by Means of Fuzzy Equivalence Relation," Mathematics, MDPI, vol. 10(24), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4648-:d:997374
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    References listed on IDEAS

    as
    1. Salvador Romaguera & Pedro Tirado, 2020. "Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results," Mathematics, MDPI, vol. 8(2), pages 1-7, February.
    2. Valentín Gregori & Juan-José Miñana & Samuel Morillas & Almanzor Sapena, 2022. "On Principal Fuzzy Metric Spaces," Mathematics, MDPI, vol. 10(16), pages 1-10, August.
    Full references (including those not matched with items on IDEAS)

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