Approximated Fuzzy p-values by Bootstrapped Fuzzy Distributions and Fuzzy Hypotheses Testing

Julien Rosset, Laurent Donzé

2024

Abstract

Although we could dispute the use of p-values, it is a standard tool used by many to know if one has to reject or not a null hypothesis. With the emergence of fuzzy data, fuzzy hypothesis testing procedures appeared. Among these testing procedures, various methods to compute crisp or fuzzy p-values arising from fuzzy data and hypotheses were investigated. However, we noticed that, despite calculating a fuzzy test statistic, none of these approaches assume a fuzzy distribution. Thus, to remedy this, we tackle the problem of finding fuzzy p-values in the context of both fuzzy data and hypotheses while considering the fuzzy distribution of the test statistic. Finding fuzzy p-values alone is not helpful if one does not know how to use them to make a decision. This is why we also provide a way to interpret fuzzy p-values and present a decision rule to reject or not the fuzzy null hypothesis. Additionally, we aim to compare this decision rule to fuzzy statistical testing procedures. We thus offer an empirical application that compares the decisions obtained from fuzzy p-values to the results given by a fuzzy hypothesis testing procedure.

Paper Citation

in Harvard Style

Rosset J. and Donzé L. (2024). Approximated Fuzzy p-values by Bootstrapped Fuzzy Distributions and Fuzzy Hypotheses Testing. In Proceedings of the 16th International Joint Conference on Computational Intelligence - Volume 1: FCTA; ISBN 978-989-758-721-4, SciTePress, pages 387-395. DOI: 10.5220/0012888300003837

in Bibtex Style

@conference{fcta24,
author={Julien Rosset and Laurent Donzé},
title={Approximated Fuzzy p-values by Bootstrapped Fuzzy Distributions and Fuzzy Hypotheses Testing},
booktitle={Proceedings of the 16th International Joint Conference on Computational Intelligence - Volume 1: FCTA},
year={2024},
pages={387-395},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012888300003837},
isbn={978-989-758-721-4},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 16th International Joint Conference on Computational Intelligence - Volume 1: FCTA
TI - Approximated Fuzzy p-values by Bootstrapped Fuzzy Distributions and Fuzzy Hypotheses Testing
SN - 978-989-758-721-4
AU - Rosset J.
AU - Donzé L.
PY - 2024
SP - 387
EP - 395
DO - 10.5220/0012888300003837
PB - SciTePress