Decomposition and Arrow-Like Aggregation of Fuzzy Preferences

Abstract

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.

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