# Fuzzy Least Squares and Fuzzy Orthogonal Least Squares Linear Regressions

### Julien Rosset, Laurent Donzé

#### 2023

#### 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.

Download#### Paper Citation

#### in Harvard Style

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 - Volume 1: FCTA*; ISBN 978-989-758-674-3, SciTePress, pages 359-368. DOI: 10.5220/0012182700003595

#### in Bibtex Style

@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 - Volume 1: FCTA},

year={2023},

pages={359-368},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0012182700003595},

isbn={978-989-758-674-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 15th International Joint Conference on Computational Intelligence - Volume 1: FCTA

TI - Fuzzy Least Squares and Fuzzy Orthogonal Least Squares Linear Regressions

SN - 978-989-758-674-3

AU - Rosset J.

AU - Donzé L.

PY - 2023

SP - 359

EP - 368

DO - 10.5220/0012182700003595

PB - SciTePress