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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| Published in: | Fuzzy sets and systems Vol. 467 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
15.09.2023
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| Subjects: | |
| ISSN: | 0165-0114, 1872-6801 |
| Online Access: | Get full text |
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| Summary: | 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. |
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| ISSN: | 0165-0114 1872-6801 |
| DOI: | 10.1016/j.fss.2023.02.015 |