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

^*Corresponding author for this work

Hamburg University of Technology

Research output: Contributions to collected editions/works › Article in conference proceedings › Research › peer-review

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.

Original language	English
Title of host publication	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
Editors	Jose M. Alonso, Marek Reformat, Humberto Bustince
Number of pages	4
Publisher	Atlantis Press
Publication date	10.2015
Pages	137-140
ISBN (Print)	978-1-5108-0807-2
DOIs	https://doi.org/10.2991/ifsa-eusflat-15.2015.12
Publication status	Published - 10.2015
Externally published	Yes
Event	Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology - IFSA-EUSFLAT 2015 - Gijón, Asturias, Spain Duration: 30.06.2015 → 03.07.2015 https://www.e3sensory.eu/ifsa-eusflat-2015/

Bibliographical note

Research areas and keywords

Engineering
Decomposition of fuzzy numbers
α-cuts
numerical fuzzy calculus

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10.2991/ifsa-eusflat-15.2015.12Licence: CC BY-NC

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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 (Eds.), 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 (pp. 137-140). (Advances in Intelligent Systems Research; Vol. 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. editor / Jose M. Alonso ; Marek Reformat ; Humberto Bustince. Atlantis Press, 2015. pp. 137-140 (Advances in Intelligent Systems Research).

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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",

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

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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",

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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 (eds), 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, vol. 89, Atlantis Press, pp. 137-140, Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology - IFSA-EUSFLAT 2015, Gijón, Asturias, Spain, 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. ed. / Jose M. Alonso; Marek Reformat; Humberto Bustince. Atlantis Press, 2015. p. 137-140 (Advances in Intelligent Systems Research; Vol. 89).

Research output: Contributions to collected editions/works › Article in conference proceedings › Research › peer-review

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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

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DO - 10.2991/ifsa-eusflat-15.2015.12

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SN - 978-1-5108-0807-2

T3 - Advances in Intelligent Systems Research

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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

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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, editors, 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. p. 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

Abstract

Bibliographical note

Research areas and keywords

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