# Fuzzy Confidence Intervals by the Likelihood Ratio with Bootstrapped Distribution

### Rédina Berkachy, Laurent Donzé

#### 2020

#### Abstract

We propose a complete practical procedure to construct a fuzzy confidence interval by the likelihood method where the observations and the hypotheses are considered to be fuzzy. We use the bootstrap technique to estimate the distribution of the likelihood ratio. For this step of the process, we mainly expose two algorithms: the first one consists on simply randomly drawing the bootstrap samples, and the second one is based on drawing observations by preserving the location and dispersion measures of the primary data set. This is achieved in accordance with a new metric written as dθ? SGD. It is built on the basis of the known signed distance measure. We also provide a simulation study to measure the performance of both bootstrap algorithms and their influence on the constructed confidence intervals. We illustrate our method via a numerical application where we construct fuzzy confidence intervals by the traditional and the defended methods. The aim is to highlight important differences between them.

Download#### Paper Citation

#### in Harvard Style

Berkachy R. and Donzé L. (2020). **Fuzzy Confidence Intervals by the Likelihood Ratio with Bootstrapped Distribution**. In *Proceedings of the 12th International Joint Conference on Computational Intelligence (IJCCI 2020) - Volume 1: FCTA*; ISBN 978-989-758-475-6, SciTePress, pages 231-242. DOI: 10.5220/0010023602310242

#### in Bibtex Style

@conference{fcta20,

author={Rédina Berkachy and Laurent Donzé},

title={Fuzzy Confidence Intervals by the Likelihood Ratio with Bootstrapped Distribution},

booktitle={Proceedings of the 12th International Joint Conference on Computational Intelligence (IJCCI 2020) - Volume 1: FCTA},

year={2020},

pages={231-242},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010023602310242},

isbn={978-989-758-475-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 12th International Joint Conference on Computational Intelligence (IJCCI 2020) - Volume 1: FCTA

TI - Fuzzy Confidence Intervals by the Likelihood Ratio with Bootstrapped Distribution

SN - 978-989-758-475-6

AU - Berkachy R.

AU - Donzé L.

PY - 2020

SP - 231

EP - 242

DO - 10.5220/0010023602310242

PB - SciTePress