A generalization of the Choquet integral defined in terms of the Mobius transform
Fecha
2020Autor
Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Identificador del proyecto
ES/1PE/TIN2016-77356-P
Impacto
|
10.1109/TFUZZ.2019.2933803
Resumen
In this article, we propose a generalization of the Choquet integral, starting fromits definition in terms of the Mobius transform. We modify the product on R considered in the Lovasz extension form of the Choquet integral into a function F, and we discuss the properties of this new functional. For a fixed n, a complete description of all F yielding an n-ary aggregation function with a fixed diag ...
[++]
In this article, we propose a generalization of the Choquet integral, starting fromits definition in terms of the Mobius transform. We modify the product on R considered in the Lovasz extension form of the Choquet integral into a function F, and we discuss the properties of this new functional. For a fixed n, a complete description of all F yielding an n-ary aggregation function with a fixed diagonal section, independent of the considered fuzzy measure, is given, and several particular examples are presented. Finally, all functions F yielding an aggregation function, independent of the number n of inputs and of the considered fuzzy measure, are characterized, and related aggregation functions are shown to be just the Choquet integrals over the distorted inputs. [--]
Materias
Aggregation function,
Choquet integral,
Fuzzy measure,
Mobius transform
Editor
IEEE
Publicado en
IEEE Transactions on Fuzzy Systems, 28 (10) 2313-2319
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 work was supported in part by the Slovak Research and Development Agency under Contract APVV-17-0066, Grant VEGA 1/0682/16, and Grant VEGA 1/0614/18, and in part by the Grant Agency of the Czech Republic under Project 18-06915S and Project TIN2016-77356-P (AEI/FEDER,UE).