Decomposition and arrow-like aggregation of fuzzy preferences

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...

Full description

Bibliographic Details
Authors: Raventós Pujol, Armajac, Campión Arrastia, María Jesús, Induráin Eraso, Esteban
Format: article
Status:Published version
Publication Date:2020
Country:España
Institution:Universidad Pública de Navarra
Repository:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/37331
Online Access:https://hdl.handle.net/2454/37331
Access Level:Open access
Keyword: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
Description
Summary: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.