Pointwise aggregation of maps: its structural functional equation and some applications to social choice theory

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 aggreg...

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Detalles Bibliográficos
Autores: Miguel Turullols, Laura de, Campión Arrastia, María Jesús, Candeal, Juan Carlos, Induráin Eraso, Esteban, Paternain Dallo, Daniel
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2017
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:2454/25495
Acceso en línea:https://hdl.handle.net/2454/25495
Access Level:acceso abierto
Palabra clave:Aggregation operators
Functional equations
Pointwise aggregation
Real-valued functions
Type-2fuzzy sets
Applications to social choice
Descripción
Sumario: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.