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] Gagolewski, Marek [verfasserIn] Grzegorzewski, Przemyslaw [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Schlagwörter: |
Approximation of fuzzy numbers |
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| Übergeordnetes Werk: |
Enthalten in: Soft Computing - Springer-Verlag, 2003, 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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SPR006507263 |
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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)SPR006507263 (SPR)s00500-019-03800-2-e DE-627 ger DE-627 rakwb eng Coroianu, Lucian verfasserin aut Piecewise linear approximation of fuzzy numbers: algorithms, arithmetic operations and stability of characteristics 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 (dpeaa)DE-He213 Calculations on fuzzy numbers (dpeaa)DE-He213 Characteristics of fuzzy numbers (dpeaa)DE-He213 Fuzzy number (dpeaa)DE-He213 Piecewise linear approximation (dpeaa)DE-He213 Gagolewski, Marek verfasserin aut Grzegorzewski, Przemyslaw verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 23(2019), 19 vom: 14. Feb., Seite 9491-9505 (DE-627)SPR006469531 nnns volume:23 year:2019 number:19 day:14 month:02 pages:9491-9505 https://dx.doi.org/10.1007/s00500-019-03800-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 23 2019 19 14 02 9491-9505 |
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10.1007/s00500-019-03800-2 doi (DE-627)SPR006507263 (SPR)s00500-019-03800-2-e DE-627 ger DE-627 rakwb eng Coroianu, Lucian verfasserin aut Piecewise linear approximation of fuzzy numbers: algorithms, arithmetic operations and stability of characteristics 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 (dpeaa)DE-He213 Calculations on fuzzy numbers (dpeaa)DE-He213 Characteristics of fuzzy numbers (dpeaa)DE-He213 Fuzzy number (dpeaa)DE-He213 Piecewise linear approximation (dpeaa)DE-He213 Gagolewski, Marek verfasserin aut Grzegorzewski, Przemyslaw verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 23(2019), 19 vom: 14. Feb., Seite 9491-9505 (DE-627)SPR006469531 nnns volume:23 year:2019 number:19 day:14 month:02 pages:9491-9505 https://dx.doi.org/10.1007/s00500-019-03800-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 23 2019 19 14 02 9491-9505 |
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10.1007/s00500-019-03800-2 doi (DE-627)SPR006507263 (SPR)s00500-019-03800-2-e DE-627 ger DE-627 rakwb eng Coroianu, Lucian verfasserin aut Piecewise linear approximation of fuzzy numbers: algorithms, arithmetic operations and stability of characteristics 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 (dpeaa)DE-He213 Calculations on fuzzy numbers (dpeaa)DE-He213 Characteristics of fuzzy numbers (dpeaa)DE-He213 Fuzzy number (dpeaa)DE-He213 Piecewise linear approximation (dpeaa)DE-He213 Gagolewski, Marek verfasserin aut Grzegorzewski, Przemyslaw verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 23(2019), 19 vom: 14. Feb., Seite 9491-9505 (DE-627)SPR006469531 nnns volume:23 year:2019 number:19 day:14 month:02 pages:9491-9505 https://dx.doi.org/10.1007/s00500-019-03800-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 23 2019 19 14 02 9491-9505 |
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10.1007/s00500-019-03800-2 doi (DE-627)SPR006507263 (SPR)s00500-019-03800-2-e DE-627 ger DE-627 rakwb eng Coroianu, Lucian verfasserin aut Piecewise linear approximation of fuzzy numbers: algorithms, arithmetic operations and stability of characteristics 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 (dpeaa)DE-He213 Calculations on fuzzy numbers (dpeaa)DE-He213 Characteristics of fuzzy numbers (dpeaa)DE-He213 Fuzzy number (dpeaa)DE-He213 Piecewise linear approximation (dpeaa)DE-He213 Gagolewski, Marek verfasserin aut Grzegorzewski, Przemyslaw verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 23(2019), 19 vom: 14. Feb., Seite 9491-9505 (DE-627)SPR006469531 nnns volume:23 year:2019 number:19 day:14 month:02 pages:9491-9505 https://dx.doi.org/10.1007/s00500-019-03800-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 23 2019 19 14 02 9491-9505 |
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10.1007/s00500-019-03800-2 doi (DE-627)SPR006507263 (SPR)s00500-019-03800-2-e DE-627 ger DE-627 rakwb eng Coroianu, Lucian verfasserin aut Piecewise linear approximation of fuzzy numbers: algorithms, arithmetic operations and stability of characteristics 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 (dpeaa)DE-He213 Calculations on fuzzy numbers (dpeaa)DE-He213 Characteristics of fuzzy numbers (dpeaa)DE-He213 Fuzzy number (dpeaa)DE-He213 Piecewise linear approximation (dpeaa)DE-He213 Gagolewski, Marek verfasserin aut Grzegorzewski, Przemyslaw verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 23(2019), 19 vom: 14. Feb., Seite 9491-9505 (DE-627)SPR006469531 nnns volume:23 year:2019 number:19 day:14 month:02 pages:9491-9505 https://dx.doi.org/10.1007/s00500-019-03800-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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. |
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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. |
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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. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR006507263</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20201124002912.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201005s2019 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00500-019-03800-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR006507263</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00500-019-03800-2-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Coroianu, Lucian</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Piecewise linear approximation of fuzzy numbers: algorithms, arithmetic operations and stability of characteristics</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2019</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="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. 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Feb., Seite 9491-9505</subfield><subfield code="w">(DE-627)SPR006469531</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:23</subfield><subfield code="g">year:2019</subfield><subfield code="g">number:19</subfield><subfield code="g">day:14</subfield><subfield code="g">month:02</subfield><subfield code="g">pages:9491-9505</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s00500-019-03800-2</subfield><subfield code="z">kostenfrei</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">23</subfield><subfield code="j">2019</subfield><subfield code="e">19</subfield><subfield code="b">14</subfield><subfield code="c">02</subfield><subfield code="h">9491-9505</subfield></datafield></record></collection>
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