Fuzzy Arrovian Theorems when preferences are complete

TL;DR

This paper explores the aggregation of fuzzy preferences in societies, characterizing models where preferences are complete and transitive under various t-norms, extending classical Arrovian theorems to fuzzy settings.

Contribution

It introduces a framework for fuzzy preference aggregation with complete preferences and characterizes possibility and impossibility results using models defined by crisp relations.

Findings

Characterization of models with complete fuzzy preferences

Extension of Arrovian impossibility results to fuzzy preferences

Application of Kirman and Sondermann's results to fuzzy preference models

Abstract

In this paper we study the aggregation of fuzzy preferences on non-necessarily finite societies. We characterize in terms of possibility and impossibility a family of models of complete preferences in which the transitivity is defined for any t-norm. For that purpose, we have described each model by means of some crisp binary relations and we have applied the results obtained by Kirman and Sondermann.