Statistical depth for fuzzy sets

Autor: Luis González-De La Fuente, Alicia Nieto-Reyes, Pedro Terán
Přispěvatelé: Universidad de Cantabria
Rok vydání: 2022
Předmět:
Zdroj: Scopus
RUO. Repositorio Institucional de la Universidad de Oviedo
Universidad de las Islas Baleares
Fuzzy Sets and Systems, 2022, 443(Part A), 58-86
ISSN: 0165-0114
DOI: 10.1016/j.fss.2021.09.015
Popis: Statistical depth functions provide a way to order the elements of a space by their centrality in a probability distribution. That has been very successful for generalizing non-parametric order-based statistical procedures from univariate to multivariate and (more recently) to functional spaces. We introduce two general definitions of statistical depth which are adapted to fuzzy data. For that purpose, two concepts of symmetric fuzzy random variables are introduced and studied. Furthermore, a generalization of Tukey's halfspace depth to the fuzzy setting is presented and proved to satisfy the above notions, through a detailed study of its properties. A. Nieto-Reyes and L. Gonzalez are supported by the Spanish Ministerio de Economía, Industria y Competitividad grant MTM2017-86061-C2-2-P. P. Terán is supported by the Ministerio de Economía y Competitividad grant MTM2015-63971-P, the Ministerio de Ciencia, Innovación y Universidades grant PID2019-104486GB-I00 and the Consejería de Empleo, Industria y Turismo del Principado de Asturias grant GRUPIN-IDI2018-000132.
Databáze: OpenAIRE
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