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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Vydané v:	Mathematics (Basel) Ročník 11; číslo 10; s. 2331
Hlavní autori:	Xu, Yanyan, Sun, Lu, Li, Hao, Chen, Guanggui
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Basel MDPI AG 01.05.2023
Predmet:	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
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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.
AbstractList	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.
Audience	Academic
Author	Xu, Yanyan Chen, Guanggui Sun, Lu Li, Hao
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Cites_doi	10.1016/0165-0114(92)90338-5 10.21123/bsj.2021.18.4.1204 10.3390/sym11070923 10.1016/j.fss.2015.02.003 10.1080/03081079.2019.1608985 10.1016/0165-0114(84)90034-4 10.1016/S0165-0114(02)00274-9 10.1016/j.fss.2004.05.004 10.1016/j.fss.2009.10.004 10.30684/etj.37.1B.5 10.1016/S0019-9958(65)90241-X 10.3390/math7101003 10.21123/bsj.2019.16.1.0104 10.1142/S1793005720500118 10.2307/1968691
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Title	The Fuzzy Width Theory in the Finite-Dimensional Space and Sobolev Space
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