Directional monotonicity of multidimensional fusion functions with respect to admissible orders
Consultable a partir de
2025-09-15
Fecha
2023Versión
Acceso embargado / Sarbidea bahitua dago
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Identificador del proyecto
Impacto
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10.1016/j.fss.2023.03.001
Resumen
The notion of directional monotonicity emerged as a relaxation of the monotonicity condition of aggregation functions. As the extension of aggregation functions to fuse more complex information than numeric data, directional monotonicity was extended to the framework of multidimensional data, with respect to the product order, which is a partial order. In this work, we present the notion of admis ...
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The notion of directional monotonicity emerged as a relaxation of the monotonicity condition of aggregation functions. As the extension of aggregation functions to fuse more complex information than numeric data, directional monotonicity was extended to the framework of multidimensional data, with respect to the product order, which is a partial order. In this work, we present the notion of admissible order for multidimensional data and we define the concept of directional monotonicity for multidimensional fusion functions with respect to an admissible order. Moreover, we study the main properties of directionally monotone functions in this new context. We conclude that, while some of the properties are still valid (e.g. the set of directions of increasingness is still closed under convex combinations), some of the main ones no longer hold (e.g. there does not exist a finite set of directions that characterize standard monotonicity in terms of directional monotonicity). [--]
Materias
Aggregation function,
Directional monotonicity,
Fusion function,
Interval-valued data,
Multidimensional data
Editor
Elsevier
Publicado en
Fuzzy Sets and Systems, 467 (2023) 108498
Departamento
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. Institute of Smart Cities - ISC
Versión del editor
Entidades Financiadoras
This work has been funded by the Spanish ministry MCIN , with the project PID2019-108392GB-I00/AEI/10.13039/501100011033, by the Public University of Navarra under the project PJUPNA25-2022 and by the grant APVV-18-0052 by the Slovak Research and Development Agency .