Liberalism and dictatorship in the problem of fuzzy classification

We investigate two related problems of categorization of alternatives. We are particularly concerned about liberalism and dictatorship, two noteworthy and opposing principles, in the context of fuzzy expressions of the opinions. First we study the problem of self-distributing the individuals in a society among fixed classes or categories. We identify a restriction on the fuzzy expression of the opinions that relies on Ruspini partitions, such that two characterizations of liberalism hold true. Then we show that similar axiomatizations can be produced with a more general structure of the fuzzy inputs, where the individuals are allowed to use ϵ-partitions. Secondly we study plausible sufficient conditions for the existence of dictators when a group of agents assigns degrees of membership of objects to a fixed list of classes.