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Open AccessArticle

An Abstract Result on Projective Aggregation Functions

Departamento de Análisis Económico, Universidad de Zaragoza, Gran Vía 2, 50005 Zaragoza, Spain
Axioms 2018, 7(1), 17; https://doi.org/10.3390/axioms7010017
Received: 1 March 2018 / Revised: 13 March 2018 / Accepted: 19 March 2018 / Published: 20 March 2018
(This article belongs to the Special Issue New Trends in Fuzzy Set Theory and Related Items)
A general characterization result of projective aggregation functions is shown, the proof of which makes use of the celebrated Arrow’s theorem, thus providing a link between aggregation functions theory and social choice theory. The result can be viewed as a generalization of a theorem obtained by Kim (1990) for real-valued aggregation functions defined on the n-dimensional Euclidean space in the context of measurement theory. In addition, two applications of the core theorem of the article are shown. The first is a simple extension of the main result to the context of multi-valued aggregation functions. The second offers a new characterization of projective bijection aggregators, thus connecting aggregation operators theory with social choice. View Full-Text
Keywords: aggregation functions; aggregation operators; Arrow’s theorem aggregation functions; aggregation operators; Arrow’s theorem
MDPI and ACS Style

Candeal, J.C. An Abstract Result on Projective Aggregation Functions. Axioms 2018, 7, 17.

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