Model Inversion using Extended Gradual Intervals Arithmetic

DOI

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.

Copyright

© 2011, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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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 (EUSFLAT-11)
PB  - Atlantis Press
SP  - 757
EP  - 762
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2011.58
DO  - 10.2991/eusflat.2011.58
ID  - Boukezzoula2011/08
ER  -