A new view on Arrovian dictatorship in a fuzzy setting

In this note, we obtain new Arrovian results in the setting where the preferences of individuals are fuzzy and no properties of asymmetry are required. Dealing with a society made of possibly infinitely many individuals, we obtain the existence of a unique ultrafilter of decisive coalitions for every Fuzzy Social Welfare Function that obeys to Arrow's like axioms. Then, we deduce new impossibility and possibility results.