Pointwise aggregation of maps: its structural functional equation and some applications to social choice theory
Fecha
2017Autor
Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Identificador del proyecto
Impacto
|
10.1016/j.fss.2016.05.010
Resumen
We study a structural functional equation that is directly related to the pointwise aggregation of a finite number of maps from a given nonempty set into another. First we establish links between pointwise aggregation and invariance properties. Then, paying attention to the particular case of aggregation operators of a finite number of real-valued functions, we characterize several special kinds ...
[++]
We study a structural functional equation that is directly related to the pointwise aggregation of a finite number of maps from a given nonempty set into another. First we establish links between pointwise aggregation and invariance properties. Then, paying attention to the particular case of aggregation operators of a finite number of real-valued functions, we characterize several special kinds of aggregation operators as strictly monotone modifications of projections. As a case study, we introduce a first approach of type-2fuzzy sets via fusion operators. We develop some applications and possible uses related to the analysis of properties of social evaluation functionals in social choice, showing that those functionals can actually be described by using methods that derive from this setting. [--]
Materias
Aggregation operators,
Functional equations,
Pointwise aggregation,
Real-valued functions,
Type-2fuzzy sets,
Applications to social choice
Editor
Elsevier
Publicado en
Fuzzy Sets and Systems 325 (2017) 137–151
Departamento
Universidad Pública de Navarra. Departamento de Automática y Computación /
Universidad Pública de Navarra. Departamento de Matemáticas /
Nafarroako Unibertsitate Publikoa. Automatika eta Konputazioa Saila /
Nafarroako Unibertsitate Publikoa. Matematika Saila
Versión del editor
Entidades Financiadoras
This work has been supported by the research projects ECO2012-34828,
MTM2012-37894-C02-02, MTM2015-63608-P, TIN2013-47605-P, TIN2011-29520 (Spain) and the Research Services of the Public University of Navarre.