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Open AccessArticle

Decomposition and Arrow-Like Aggregation of Fuzzy Preferences

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Institute for Advanced Research in Business and Economics and Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain
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Institute for Advanced Materials and Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 436; https://doi.org/10.3390/math8030436 (registering DOI)
Received: 4 February 2020 / Revised: 11 March 2020 / Accepted: 12 March 2020 / Published: 17 March 2020
(This article belongs to the Special Issue Group Decision Making Based on Artificial Intelligence)
We 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. View Full-Text
Keywords: Arrow’s impossibility theorems; mathematical social choice; fuzzy preferences; decomposition of preferences; aggregation of individual profiles; social rules; Arrovian models; Paretian property; independence of irrelevant alternatives; dictatorship Arrow’s impossibility theorems; mathematical social choice; fuzzy preferences; decomposition of preferences; aggregation of individual profiles; social rules; Arrovian models; Paretian property; independence of irrelevant alternatives; dictatorship
MDPI and ACS Style

Raventós-Pujol, A.; Campión, M.J.; Induráin, E. Decomposition and Arrow-Like Aggregation of Fuzzy Preferences. Mathematics 2020, 8, 436.

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