Decomposition and Arrow-Like Aggregation of Fuzzy Preferences

• Main Authors: Armajac Raventós-Pujol, María J. Campión, Esteban Induráin
• Format: Article
• Language: English
• Published: MDPI AG 2020-03-01
• Series: Mathematics
• Subjects: 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
• Online Access: https://www.mdpi.com/2227-7390/8/3/436

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.