Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11)

Model Inversion using Extended Gradual Intervals Arithmetic

Authors
Reda Boukezzoula, Laurent Foulloy, Sylvie Galichet
Corresponding Author
Reda Boukezzoula
Available Online August 2011.
DOI
https://doi.org/10.2991/eusflat.2011.58How to use a DOI?
Keywords
Fuzzy and Gradual Interval Arithmetic, Extended Gradual Intervals, Exact Inverse operators, Midpoint-Radius Representation, Gradual Interval Model Inversion.
Abstract
Recently, gradual numbers have been introduced as a means of extending standard interval computation methods to fuzzy and gradual intervals. However, it is well known that the practical use of standard interval arithmetic operators, just as their fuzzy extension, gives results more imprecise than necessary. In this paper, we combine the concepts of gradual numbers and Kaucher arithmetic on extended intervals to define extended gradual interval arithmetic where subtraction and division operators are respectively the inverse operators of the addition and the multiplication. They are applied to a control problem based on the inversion of a linear model.
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This is an open access article distributed under the CC BY-NC license.

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Proceedings
Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology
Part of series
Advances in Intelligent Systems Research
Publication Date
August 2011
ISBN
978-90-78677-00-0
ISSN
1951-6851
DOI
https://doi.org/10.2991/eusflat.2011.58How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - CONF
AU  - Reda Boukezzoula
AU  - Laurent Foulloy
AU  - Sylvie Galichet
PY  - 2011/08
DA  - 2011/08
TI  - Model Inversion using Extended Gradual Intervals Arithmetic
BT  - Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology
PB  - Atlantis Press
SP  - 757
EP  - 762
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2011.58
DO  - https://doi.org/10.2991/eusflat.2011.58
ID  - Boukezzoula2011/08
ER  -