From fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets: a unified view of different axiomatic measures
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión aceptada / Onetsi den bertsioa
ES/1PE/TIN2014-56967-R ES/1PE/TIN2016-77356-P ES/2PE/TIN2017-84804-R
We examine a broad collection of axiomatic definitions from various and diverse contexts, within the domain of fuzzy sets. We evaluate their respective extensions to the case of interval-valued fuzzy sets and intuitionistic fuzzy sets, from a purely formal point of view. We conclude that a large number of such extensions follow similar formal procedures This fact allows us to formulate a general ... [++]
We examine a broad collection of axiomatic definitions from various and diverse contexts, within the domain of fuzzy sets. We evaluate their respective extensions to the case of interval-valued fuzzy sets and intuitionistic fuzzy sets, from a purely formal point of view. We conclude that a large number of such extensions follow similar formal procedures This fact allows us to formulate a general procedure which encompasses all the reviewed extensions as particular cases of it. The new general formulation allows us to identify three different procedures to derive the corresponding extension to the field of interval-valued fuzzy sets or to the field of intuitionistic fuzzy sets from a specific real-valued measure in the context of fuzzy sets. These three processes agglutinate a multitude of particular constructions found in the literature. [--]
IEEE Transactions on Fuzzy Systems, 27 (2), 362-371, 2019
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas / Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila / Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa. ISC - Institute of Smart Cities
This work is partially supported by TIN2014-56967-R, TIN2016-77356-P, TIN2017-84804-R (Spanish Ministry of Science and Innovation) and FC-15-GRUPIN14-073 (Regional Ministry of the Principality of Asturias).
Appears in Collections
Items in Academica-e are protected by copyright with all rights reserved, unless otherwise noted.
Showing items related by title, author, creator and subject.
Bustince Sola, Humberto ; Barrenechea Tartas, Edurne ; Pagola Barrio, Miguel ; Fernández Fernández, Francisco Javier ; Xu, Zeshui; Bedregal, Benjamin; Montero, Javier; Hagras, Hani; Herrera, Francisco; Baets, Bernard de (IEEE, 2016) Artículo / ArtikuluaIn this work we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the ...
A theorem for constructing interval-valued intuitionistic fuzzy sets from intuitionistic fuzzy sets Bustince Sola, Humberto ; Burillo López, Pedro (Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1995) Artículo / ArtikuluaIn this paper we present a theorem that allows us to construct interval-valued intuitionistic fuzzy sets from intuitionistic fuzzy sets. We also study the way of recovering intuitionistic fuzzy sets used in the construction ...
Bustince Sola, Humberto ; Mohedano Salillas, Victoria (Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1997) Contribución a congreso / Biltzarrerako ekarpenaIn this paper form the definition of intuitionistic fuzzy sets we analyze the intuitionistic fuzzy generators and the complementation in these sets. We start by defining the intuitionistic fuzzy generators in order to then ...