Simplicial depths for fuzzy random variables

González de la Fuente, Luis; Nieto Reyes, Alicia; Terán, Pedro

doi:10.1016/j.fss.2023.108678

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Identificadores

URI: https://hdl.handle.net/10902/32316

DOI: 10.1016/j.fss.2023.108678

ISSN: 0165-0114

ISSN: 1872-6801

Fecha

2023-11

Derechos

Publicado en

Fuzzy Sets and Systems, 2023, 471, 108678

Editorial

Elsevier

Enlace a la publicación

https://doi.org/10.1016/j.fss.2023.108678

Palabras clave

Fuzzy data

Fuzzy random variable

Nonparametric statistics

Statistical depth

Simplicial Depth

Resumen/Abstract

The recently defined concept of statistical depth function for fuzzy sets provides a theoretical framework for ordering fuzzy sets with respect to the distribution of a fuzzy random variable. One of the most used and studied statistical depth functions for multivariate data is simplicial depth, based on multivariate simplices. We introduce a notion of pseudosimplices generated by fuzzy sets and propose three generalizations of simplicial depth to fuzzy sets. Their theoretical properties are analyzed and the behavior of the proposals is illustrated through a study of both synthetic and real data.

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©2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Excepto si se señala otra cosa, la licencia del ítem se describe como ©2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).