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

Yanyan Xu, Lu Sun, Hao Li and Guanggui Chen ()
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Yanyan Xu: School of Science, Xihua University, Chengdu 610039, China
Lu Sun: School of Science, Xihua University, Chengdu 610039, China
Hao Li: School of Science, Xihua University, Chengdu 610039, China
Guanggui Chen: Graduate School, Xihua University, Chengdu 610039, China

Mathematics, 2023, vol. 11, issue 10, 1-15

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.

Keywords: fuzzy norm; ? -fuzzy distance; fuzzy Kolmogorov n -width; fuzzy linear n -width (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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