Approximations of n-dimensional fuzzy numbers by using α − β-knots piecewise linear fuzzy n-cell numbers

As we all know, when describing some complex fuzzy events, n-dimensional fuzzy numbers are more effective and reasonable. However, at present, due to the complex structure of n-dimensional fuzzy numbers, there are few investigations about approximations of n-dimensional fuzzy numbers. So, in this pa...

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Veröffentlicht in:Fuzzy sets and systems Jg. 467
Hauptverfasser: Lv, Haojie, Wang, Guixiang, Li, Chengjia
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 15.09.2023
Schlagworte:
[formula omitted]-knots piecewise linear fuzzy n-cell numbers
Approximations
Membership function
n-dimensional fuzzy numbers
Membership function
α−β-knots piecewise linear fuzzy n-cell numbers
n-dimensional fuzzy numbers
Approximations
ISSN:0165-0114, 1872-6801
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Abstract As we all know, when describing some complex fuzzy events, n-dimensional fuzzy numbers are more effective and reasonable. However, at present, due to the complex structure of n-dimensional fuzzy numbers, there are few investigations about approximations of n-dimensional fuzzy numbers. So, in this paper, we discuss the problem of approximating n-dimensional fuzzy number by using α−β-knots piecewise linear fuzzy n-cell numbers. Firstly, α−β-knots piecewise linear fuzzy n-cell numbers are defined, and the conceptions of I-nearest α−β-knots piecewise linear fuzzy approximation and II-nearest α−β-knots piecewise linear fuzzy approximation are introduced for a general n-dimensional fuzzy number. Then, most importantly, using weighted metric as a criterion, we obtain formulas to get the I-nearest α−β-knots piecewise linear fuzzy approximation and II-nearest α−β-knots piecewise linear fuzzy approximation. Finally, we give a specific example to show the reasonable and effective of the methods proposed by us.
AbstractList As we all know, when describing some complex fuzzy events, n-dimensional fuzzy numbers are more effective and reasonable. However, at present, due to the complex structure of n-dimensional fuzzy numbers, there are few investigations about approximations of n-dimensional fuzzy numbers. So, in this paper, we discuss the problem of approximating n-dimensional fuzzy number by using α−β-knots piecewise linear fuzzy n-cell numbers. Firstly, α−β-knots piecewise linear fuzzy n-cell numbers are defined, and the conceptions of I-nearest α−β-knots piecewise linear fuzzy approximation and II-nearest α−β-knots piecewise linear fuzzy approximation are introduced for a general n-dimensional fuzzy number. Then, most importantly, using weighted metric as a criterion, we obtain formulas to get the I-nearest α−β-knots piecewise linear fuzzy approximation and II-nearest α−β-knots piecewise linear fuzzy approximation. Finally, we give a specific example to show the reasonable and effective of the methods proposed by us.
ArticleNumber 108494
Author Li, Chengjia
Lv, Haojie
Wang, Guixiang
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Keywords Membership function
α−β-knots piecewise linear fuzzy n-cell numbers
n-dimensional fuzzy numbers
Approximations
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Snippet As we all know, when describing some complex fuzzy events, n-dimensional fuzzy numbers are more effective and reasonable. However, at present, due to the...
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SubjectTerms [formula omitted]-knots piecewise linear fuzzy n-cell numbers
Approximations
Membership function
n-dimensional fuzzy numbers
Title Approximations of n-dimensional fuzzy numbers by using α − β-knots piecewise linear fuzzy n-cell numbers
URI https://dx.doi.org/10.1016/j.fss.2023.02.015
Volume 467
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