From fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets: a unified view of different axiomatic measures

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 num...

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Detalles Bibliográficos
Autores: Couso, Inés, Bustince Sola, Humberto
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2019
País:España
Institución:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/36051
Acceso en línea:https://hdl.handle.net/2454/36051
Access Level:acceso abierto
Palabra clave:Interval-valued fuzzy sets
Atanassov intuitionistic fuzzy sets
Extensions of fuzzy sets
Descripción
Sumario: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.