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Endograph Metric and a Version of the Arzelà–Ascoli Theorem for Fuzzy Sets

Author

Listed:
  • Juan J. Font

    (Institut de Matemàtiques i Applicacions de Castelló (IMAC), Universitat Jaume I de Castelló, Av. Vicent Sos Baynat s/n, 12071 Castelló de la Plana, Spain)

  • Sergio Macario

    (Institut de Matemàtiques i Applicacions de Castelló (IMAC), Universitat Jaume I de Castelló, Av. Vicent Sos Baynat s/n, 12071 Castelló de la Plana, Spain)

  • Manuel Sanchis

    (Institut de Matemàtiques i Applicacions de Castelló (IMAC), Universitat Jaume I de Castelló, Av. Vicent Sos Baynat s/n, 12071 Castelló de la Plana, Spain)

Abstract

In this paper, we provide several Arzelà–Ascoli-type results on the space of all continuous functions from a Tychonoff space X into the fuzzy sets of R n , ( F U S C B ( R n ) , H e n d ) , which are upper semi-continuous and have bounded support endowed with the endograph metric. Namely, we obtain positive results when X is considered to be a k r -space and C ( X , ( F U S C B ( R n ) , H e n d ) ) is endowed with the compact open topology, as well as when we assume that X is pseudocompact and C ( X , ( F U S C B ( R n ) , H e n d ) ) is equipped with the uniform topology.

Suggested Citation

  • Juan J. Font & Sergio Macario & Manuel Sanchis, 2023. "Endograph Metric and a Version of the Arzelà–Ascoli Theorem for Fuzzy Sets," Mathematics, MDPI, vol. 11(2), pages 1-8, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:260-:d:1024580
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    References listed on IDEAS

    as
    1. Yang Liu & Baoding Liu, 2022. "Residual analysis and parameter estimation of uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 513-530, December.
    2. Ahmad Hosseini & Mir Saman Pishvaee, 2022. "Capacity reliability under uncertainty in transportation networks: an optimization framework and stability assessment methodology," Fuzzy Optimization and Decision Making, Springer, vol. 21(3), pages 479-512, September.
    3. Zand, Behnam & Ghaderi, Pedram & Amini, Fereidoun, 2023. "Structural system identification via synchronization technique and fuzzy logic," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 174-188.
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