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The Fuzzy Width Theory in the Finite-Dimensional Space and Sobolev Space

Author

Listed:
  • Yanyan Xu

    (School of Science, Xihua University, Chengdu 610039, China
    These authors contributed equally to this work.)

  • Lu Sun

    (School of Science, Xihua University, Chengdu 610039, China
    These authors contributed equally to this work.)

  • Hao Li

    (School of Science, Xihua University, Chengdu 610039, China
    These authors contributed equally to this work.)

  • Guanggui Chen

    (Graduate School, Xihua University, Chengdu 610039, China)

Abstract

This paper aims to fuzzify the width problem of classical approximation theory. New concepts of fuzzy Kolmogorov n -width and fuzzy linear n -width are introduced on the basis of α -fuzzy distance which is induced by the fuzzy norm. Furthermore, the relationship between the classical widths in linear normed space and the fuzzy widths in fuzzy linear normed space is discussed. Finally, the exact asymptotic orders of the fuzzy Kolmogorov n -width and fuzzy linear n -width corresponding to a given fuzzy norm in finite-dimensional space and Sobolev space are estimated.

Suggested Citation

  • Yanyan Xu & Lu Sun & Hao Li & Guanggui Chen, 2023. "The Fuzzy Width Theory in the Finite-Dimensional Space and Sobolev Space," Mathematics, MDPI, vol. 11(10), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2331-:d:1148616
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    References listed on IDEAS

    as
    1. Ju Myung Kim & Keun Young Lee, 2019. "Approximation Properties in Felbin Fuzzy Normed Spaces," Mathematics, MDPI, vol. 7(10), pages 1-14, October.
    2. Mami Sharma & Debajit Hazarika, 2020. "Fuzzy Bounded Linear Operator in Fuzzy Normed Linear Spaces and its Fuzzy Compactness," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 177-193, March.
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