Piecewise linear approximation of fuzzy numbers: algorithms, arithmetic operations and stability of characteristics
Abstract The problem of the piecewise linear approximation of fuzzy numbers giving outputs nearest to the inputs with respect to the Euclidean metric is discussed. The results given in Coroianu et al. (Fuzzy Sets Syst 233:26–51, 2013) for the 1-knot fuzzy numbers are generalized for arbitrary n-knot...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Coroianu, Lucian [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Schlagwörter: |
Approximation of fuzzy numbers |
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| Anmerkung: |
© The Author(s) 2019 |
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| Übergeordnetes Werk: |
Enthalten in: Soft computing - Springer Berlin Heidelberg, 1997, 23(2019), 19 vom: 14. Feb., Seite 9491-9505 |
|---|---|
| Übergeordnetes Werk: |
volume:23 ; year:2019 ; number:19 ; day:14 ; month:02 ; pages:9491-9505 |
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| DOI / URN: |
10.1007/s00500-019-03800-2 |
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OLC2034900359 |
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| 520 | |a Abstract The problem of the piecewise linear approximation of fuzzy numbers giving outputs nearest to the inputs with respect to the Euclidean metric is discussed. The results given in Coroianu et al. (Fuzzy Sets Syst 233:26–51, 2013) for the 1-knot fuzzy numbers are generalized for arbitrary n-knot ($$n\ge 2$$) piecewise linear fuzzy numbers. Some results on the existence and properties of the approximation operator are proved. Then, the stability of some fuzzy number characteristics under approximation as the number of knots tends to infinity is considered. Finally, a simulation study concerning the computer implementations of arithmetic operations on fuzzy numbers is provided. Suggested concepts are illustrated by examples and algorithms ready for the practical use. This way, we throw a bridge between theory and applications as the latter ones are so desired in real-world problems. | ||
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10.1007/s00500-019-03800-2 doi (DE-627)OLC2034900359 (DE-He213)s00500-019-03800-2-p DE-627 ger DE-627 rakwb eng 004 VZ 004 VZ 11 ssgn Coroianu, Lucian verfasserin aut Piecewise linear approximation of fuzzy numbers: algorithms, arithmetic operations and stability of characteristics 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2019 Abstract The problem of the piecewise linear approximation of fuzzy numbers giving outputs nearest to the inputs with respect to the Euclidean metric is discussed. The results given in Coroianu et al. (Fuzzy Sets Syst 233:26–51, 2013) for the 1-knot fuzzy numbers are generalized for arbitrary n-knot ($$n\ge 2$$) piecewise linear fuzzy numbers. Some results on the existence and properties of the approximation operator are proved. Then, the stability of some fuzzy number characteristics under approximation as the number of knots tends to infinity is considered. Finally, a simulation study concerning the computer implementations of arithmetic operations on fuzzy numbers is provided. Suggested concepts are illustrated by examples and algorithms ready for the practical use. This way, we throw a bridge between theory and applications as the latter ones are so desired in real-world problems. Approximation of fuzzy numbers Calculations on fuzzy numbers Characteristics of fuzzy numbers Fuzzy number Piecewise linear approximation Gagolewski, Marek aut Grzegorzewski, Przemyslaw (orcid)0000-0002-5191-4123 aut Enthalten in Soft computing Springer Berlin Heidelberg, 1997 23(2019), 19 vom: 14. Feb., Seite 9491-9505 (DE-627)231970536 (DE-600)1387526-7 (DE-576)060238259 1432-7643 nnns volume:23 year:2019 number:19 day:14 month:02 pages:9491-9505 https://doi.org/10.1007/s00500-019-03800-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_267 GBV_ILN_2018 GBV_ILN_4277 AR 23 2019 19 14 02 9491-9505 |
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Abstract The problem of the piecewise linear approximation of fuzzy numbers giving outputs nearest to the inputs with respect to the Euclidean metric is discussed. The results given in Coroianu et al. (Fuzzy Sets Syst 233:26–51, 2013) for the 1-knot fuzzy numbers are generalized for arbitrary n-knot ($$n\ge 2$$) piecewise linear fuzzy numbers. Some results on the existence and properties of the approximation operator are proved. Then, the stability of some fuzzy number characteristics under approximation as the number of knots tends to infinity is considered. Finally, a simulation study concerning the computer implementations of arithmetic operations on fuzzy numbers is provided. Suggested concepts are illustrated by examples and algorithms ready for the practical use. This way, we throw a bridge between theory and applications as the latter ones are so desired in real-world problems. © The Author(s) 2019 |
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Abstract The problem of the piecewise linear approximation of fuzzy numbers giving outputs nearest to the inputs with respect to the Euclidean metric is discussed. The results given in Coroianu et al. (Fuzzy Sets Syst 233:26–51, 2013) for the 1-knot fuzzy numbers are generalized for arbitrary n-knot ($$n\ge 2$$) piecewise linear fuzzy numbers. Some results on the existence and properties of the approximation operator are proved. Then, the stability of some fuzzy number characteristics under approximation as the number of knots tends to infinity is considered. Finally, a simulation study concerning the computer implementations of arithmetic operations on fuzzy numbers is provided. Suggested concepts are illustrated by examples and algorithms ready for the practical use. This way, we throw a bridge between theory and applications as the latter ones are so desired in real-world problems. © The Author(s) 2019 |
| abstract_unstemmed |
Abstract The problem of the piecewise linear approximation of fuzzy numbers giving outputs nearest to the inputs with respect to the Euclidean metric is discussed. The results given in Coroianu et al. (Fuzzy Sets Syst 233:26–51, 2013) for the 1-knot fuzzy numbers are generalized for arbitrary n-knot ($$n\ge 2$$) piecewise linear fuzzy numbers. Some results on the existence and properties of the approximation operator are proved. Then, the stability of some fuzzy number characteristics under approximation as the number of knots tends to infinity is considered. Finally, a simulation study concerning the computer implementations of arithmetic operations on fuzzy numbers is provided. Suggested concepts are illustrated by examples and algorithms ready for the practical use. This way, we throw a bridge between theory and applications as the latter ones are so desired in real-world problems. © The Author(s) 2019 |
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Piecewise linear approximation of fuzzy numbers: algorithms, arithmetic operations and stability of characteristics |
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Gagolewski, Marek Grzegorzewski, Przemyslaw |
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