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

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 n...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 11; no. 10; p. 2331
Main Authors: Xu, Yanyan, Sun, Lu, Li, Hao, Chen, Guanggui
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.05.2023
Subjects:
Analysis
Approximation
Dimension theory (Topology)
Fuzzy algorithms
fuzzy Kolmogorov n-width
fuzzy linear n-width
Fuzzy logic
fuzzy norm
Fuzzy sets
Fuzzy systems
Investigations
Mathematics
Norms
Sobolev space
α-fuzzy distance
China
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math11102331