Fuzzy Least Squares and Fuzzy Orthogonal Least Squares Linear Regressions

Julien Rosset; Laurent Donzé

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Paper

Fuzzy Least Squares and Fuzzy Orthogonal Least Squares Linear Regressions

Topics: Fuzzy Methods in Data Analysis

In Proceedings of the 15th International Joint Conference on Computational Intelligence - Volume 1: FCTA, 359-368, 2023 , Rome, Italy

Authors: Julien Rosset and Laurent Donzé

Affiliation: ASAM Group, University of Fribourg, Boulevard de Pérolles 90, 1700 Fribourg, Switzerland

Keyword(s): Fuzzy Least Squares Linear Regression, Fuzzy Orthogonal Least Squares Linear Regression, Fuzzy OrthogoNality, Fuzzy Logic, Fuzzy Methods in Data Analysis.

Abstract: We examine the well known fuzzy least squares linear regression method. We discuss the constrained and unconstrained solutions. Based on the concept of fuzzy orthogonality, we propose the fuzzy orthogonal least squares method to solve fuzzy linear regression problems. We show that, in case of (fuzzy) orthogonal regressors, an important property of the least squares method remains valid. We obtain the same estimates of the parameters of the model if we regress on all regressors, or on each regressor considered separately. An empirical application illustrates our methods.

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Paper citation in several formats:

Rosset, J. and Donzé, L. (2023). Fuzzy Least Squares and Fuzzy Orthogonal Least Squares Linear Regressions. In Proceedings of the 15th International Joint Conference on Computational Intelligence - FCTA; ISBN 978-989-758-674-3; ISSN 2184-3236, SciTePress, pages 359-368. DOI: 10.5220/0012182700003595

@conference{fcta23,
author={Julien Rosset. and Laurent Donzé.},
title={Fuzzy Least Squares and Fuzzy Orthogonal Least Squares Linear Regressions},
booktitle={Proceedings of the 15th International Joint Conference on Computational Intelligence - FCTA},
year={2023},
pages={359-368},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012182700003595},
isbn={978-989-758-674-3},
issn={2184-3236},
}

TY - CONF

JO - Proceedings of the 15th International Joint Conference on Computational Intelligence - FCTA
TI - Fuzzy Least Squares and Fuzzy Orthogonal Least Squares Linear Regressions
SN - 978-989-758-674-3
IS - 2184-3236
AU - Rosset, J.
AU - Donzé, L.
PY - 2023
SP - 359
EP - 368
DO - 10.5220/0012182700003595
PB - SciTePress