Publication:
On the notion of fuzzy dispersion measure and its application to triangular fuzzy numbers

Consultable a partir de

Date

2023

Authors

Roldán López de Hierro, Antonio Francisco
Rueda, María del Mar
Roldán, Concepción

Director

Publisher

Elsevier
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión publicada / Argitaratu den bertsioa

Project identifier

AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-119478GB-I00/ES/
AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-108392GB-I00/ES/

Abstract

In this paper, based on the analysis of the most widely used dispersion measure in the real context (namely, the variance), we introduce the notion of fuzzy dispersion measure associated to a finite set of data given by fuzzy numbers. This measure is implemented as a fuzzy number, so there is no loss of information caused by any defuzzification. The proposed concept satisfies the usual properties in a genuinely fuzzy sense and it avoids limitations in terms of its geometric shape or its analytical properties: under this conception, it could have a piece of its support in the negative part of the real line. This novel notion can be interpreted as a way of fusing the information included in a fuzzy data set in order to make a decision based on its dispersion. To illustrate the main characteristics of this approach, we present an example of a fuzzy dispersion measure that allows to conclude that this new way to deal this problem is coherent, at least, from the point of view of human intuition.

Keywords

Dispersion measure, Fuzzy set, Fuzzy number, Variance, Decision making

Department

Estadística, Informática y Matemáticas / Estatistika, Informatika eta Matematika

Faculty/School

Degree

Doctorate program

Editor version

Funding entities

The authors are grateful to their universities. This paper has been supported by FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades by Project A-FQM-170-UGR20, and also by Ministerio de Ciencia e Innovación by Projects PID2020-119478GB-I00 and PID2019-108392GB-I00 (AEI/ 10.13039/501100011033).

© 2023 The Author(s). This is an open access article under the CC BY-NC-ND license.

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