Raventós Pujol, ArmajacCampión Arrastia, María JesúsInduráin Eraso, Esteban2020-07-062020-07-0620202227-739010.3390/math8030436https://academica-e.unavarra.es/handle/2454/37331We analyze the concept of a fuzzy preference on a set of alternatives, and how it can be decomposed in a triplet of new fuzzy binary relations that represent strict preference, weak preference and indifference. In this setting, we analyze the problem of aggregation of individual fuzzy preferences in a society into a global one that represents the whole society and accomplishes a shortlist of common-sense properties in the spirit of the Arrovian model for crisp preferences. We introduce a new technique that allows us to control a fuzzy preference by means of five crisp binary relations. This leads to an Arrovian impossibility theorem in this particular fuzzy setting.18 p.application/pdfeng© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.Arrow’s impossibility theoremsMathematical social choiceFuzzy preferencesDecomposition of preferencesAggregation of individual profilesSocial rulesArrovian models, Paretian propertyIndependence of irrelevant alternativesDictatorshipinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccessAcceso abierto / Sarbide irekia