A generalized α-level decomposition concept for numerical fuzzy calculus

Arthur Seibel; Josef Schlattmann

doi:10.2991/ifsa-eusflat-15.2015.12

A generalized α-level decomposition concept for numerical fuzzy calculus

Arthur Seibel^*
, Josef Schlattmann

^*Korrespondierende/r Autor/-in für diese Arbeit

Technische Universität Hamburg

Publikation: Beiträge in Sammelwerken › Aufsätze in Konferenzbänden › Forschung › Begutachtung

Abstract

This paper presents a new concept for the decomposition of fuzzy numbers into a finite number of α-cuts. Instead of subdividing the µ axis in an equidistant way, we suggest to subdivide the x axis equidistantly leading to a more efficient decomposition of the µ axis. Considering the interpolation error as a measure for the loss of information during the decomposition, our concept leads to the minimal information loss of the decomposed fuzzy numbers.

Originalsprache	Englisch
Titel	Proceedings of the 16th World Congress of the International Fuzzy Systems Association (IFSA) and 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT) 2015
Redakteure/-innen	Jose M. Alonso, Marek Reformat, Humberto Bustince
Seitenumfang	4
Herausgeber (Verlag)	Atlantis Press
Erscheinungsdatum	10.2015
Seiten	137-140
ISBN (Print)	978-1-5108-0807-2
DOIs	https://doi.org/10.2991/ifsa-eusflat-15.2015.12
Publikationsstatus	Erschienen - 10.2015
Extern publiziert	Ja
Veranstaltung	Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology - IFSA-EUSFLAT 2015 - Gijón, Asturias, Spanien Dauer: 30.06.2015 → 03.07.2015 https://www.e3sensory.eu/ifsa-eusflat-2015/

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Seibel, A., & Schlattmann, J. (2015). A generalized α-level decomposition concept for numerical fuzzy calculus. in J. M. Alonso, M. Reformat, & H. Bustince (Hrsg.), Proceedings of the 16th World Congress of the International Fuzzy Systems Association (IFSA) and 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT) 2015 (S. 137-140). (Advances in Intelligent Systems Research; Band 89). Atlantis Press. https://doi.org/10.2991/ifsa-eusflat-15.2015.12

Seibel, Arthur ; Schlattmann, Josef. / A generalized α-level decomposition concept for numerical fuzzy calculus. Proceedings of the 16th World Congress of the International Fuzzy Systems Association (IFSA) and 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT) 2015. Hrsg. / Jose M. Alonso ; Marek Reformat ; Humberto Bustince. Atlantis Press, 2015. S. 137-140 (Advances in Intelligent Systems Research).

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title = "A generalized α-level decomposition concept for numerical fuzzy calculus",

abstract = "This paper presents a new concept for the decomposition of fuzzy numbers into a finite number of α-cuts. Instead of subdividing the µ axis in an equidistant way, we suggest to subdivide the x axis equidistantly leading to a more efficient decomposition of the µ axis. Considering the interpolation error as a measure for the loss of information during the decomposition, our concept leads to the minimal information loss of the decomposed fuzzy numbers.",

keywords = "Engineering, Decomposition of fuzzy numbers, α-cuts, numerical fuzzy calculus",

author = "Arthur Seibel and Josef Schlattmann",

note = "{\textcopyright} 2015, the Authors. Published by Atlantis Press.; Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology - IFSA-EUSFLAT 2015, IFSA-EUSFLAT 2015 ; Conference date: 30-06-2015 Through 03-07-2015",

year = "2015",

month = oct,

doi = "10.2991/ifsa-eusflat-15.2015.12",

language = "English",

isbn = "978-1-5108-0807-2",

series = "Advances in Intelligent Systems Research",

publisher = "Atlantis Press",

pages = "137--140",

editor = "Alonso, \{Jose M.\} and Marek Reformat and Humberto Bustince",

booktitle = "Proceedings of the 16th World Congress of the International Fuzzy Systems Association (IFSA) and 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT) 2015",

address = "Netherlands",

url = "https://www.e3sensory.eu/ifsa-eusflat-2015/",

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Seibel, A & Schlattmann, J 2015, A generalized α-level decomposition concept for numerical fuzzy calculus. in JM Alonso, M Reformat & H Bustince (Hrsg.), Proceedings of the 16th World Congress of the International Fuzzy Systems Association (IFSA) and 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT) 2015. Advances in Intelligent Systems Research, Bd. 89, Atlantis Press, S. 137-140, Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology - IFSA-EUSFLAT 2015, Gijón, Asturias, Spanien, 30.06.15. https://doi.org/10.2991/ifsa-eusflat-15.2015.12

A generalized α-level decomposition concept for numerical fuzzy calculus. / Seibel, Arthur; Schlattmann, Josef.
Proceedings of the 16th World Congress of the International Fuzzy Systems Association (IFSA) and 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT) 2015. Hrsg. / Jose M. Alonso; Marek Reformat; Humberto Bustince. Atlantis Press, 2015. S. 137-140 (Advances in Intelligent Systems Research; Band 89).

Publikation: Beiträge in Sammelwerken › Aufsätze in Konferenzbänden › Forschung › Begutachtung

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AU - Seibel, Arthur

AU - Schlattmann, Josef

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N2 - This paper presents a new concept for the decomposition of fuzzy numbers into a finite number of α-cuts. Instead of subdividing the µ axis in an equidistant way, we suggest to subdivide the x axis equidistantly leading to a more efficient decomposition of the µ axis. Considering the interpolation error as a measure for the loss of information during the decomposition, our concept leads to the minimal information loss of the decomposed fuzzy numbers.

AB - This paper presents a new concept for the decomposition of fuzzy numbers into a finite number of α-cuts. Instead of subdividing the µ axis in an equidistant way, we suggest to subdivide the x axis equidistantly leading to a more efficient decomposition of the µ axis. Considering the interpolation error as a measure for the loss of information during the decomposition, our concept leads to the minimal information loss of the decomposed fuzzy numbers.

KW - Engineering

KW - Decomposition of fuzzy numbers

KW - α-cuts

KW - numerical fuzzy calculus

UR - https://www.proceedings.com/content/027/027013webtoc.pdf

U2 - 10.2991/ifsa-eusflat-15.2015.12

DO - 10.2991/ifsa-eusflat-15.2015.12

M3 - Article in conference proceedings

SN - 978-1-5108-0807-2

T3 - Advances in Intelligent Systems Research

SP - 137

EP - 140

BT - Proceedings of the 16th World Congress of the International Fuzzy Systems Association (IFSA) and 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT) 2015

A2 - Alonso, Jose M.

A2 - Reformat, Marek

A2 - Bustince, Humberto

PB - Atlantis Press

T2 - Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology - IFSA-EUSFLAT 2015

Y2 - 30 June 2015 through 3 July 2015

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Seibel A, Schlattmann J. A generalized α-level decomposition concept for numerical fuzzy calculus. in Alonso JM, Reformat M, Bustince H, Hrsg., Proceedings of the 16th World Congress of the International Fuzzy Systems Association (IFSA) and 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT) 2015. Atlantis Press. 2015. S. 137-140. (Advances in Intelligent Systems Research). doi: 10.2991/ifsa-eusflat-15.2015.12

A generalized α-level decomposition concept for numerical fuzzy calculus

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