A fuzzy methodology for approaching fuzzy sets of the real line by fuzzy numbers
Fecha
2021Autor
Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión publicada / Argitaratu den bertsioa
Identificador del proyecto
Impacto
|
10.1016/j.fss.2021.08.024
Resumen
In this paper we introduce a novel methodology to face the problem of finding, for every fuzzy set of the real line, a fuzzy number which can be considered as an approximation of the first one in some reasonable sense. This methodology depends on a wide variety of initial parameters that each researcher may set depending on his/her own interests. The main objective of this new methodology is to e ...
[++]
In this paper we introduce a novel methodology to face the problem of finding, for every fuzzy set of the real line, a fuzzy number which can be considered as an approximation of the first one in some reasonable sense. This methodology depends on a wide variety of initial parameters that each researcher may set depending on his/her own interests. The main objective of this new methodology is to ensure that many of the techniques that are currently available for fuzzy numbers can also be extended to the setting of fuzzy sets of the real line which are, in many ways, much more enriching. To do this, we carry out a study of the families of nested sets that can determine fuzzy numbers through their level sets. Next, we describe some of the main properties that this approximation methodology verifies and we show some examples to illustrate how the initial parameters influence the result of the approximation. [--]
Materias
Fuzzy number,
Fuzzy set approximation,
Level set,
Monotone operator,
Nonlinear operator
Editor
Elsevier
Publicado en
Fuzzy Sets and Systems
Departamento
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila
Versión del editor
Entidades Financiadoras
This manuscript has been partially supported by Junta de Andalucía by Project FQM-365 of the Andalusian CICYE, and also by Projects PID2020-119478GB-I00 and PID2019-108392GB-I00 (AEI/10.13039/501100011033 , Ministerio de Ciencia e Innovación).
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La licencia del ítem se describe como © 2021 The Authors. Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
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