Fuzzy classification aggregation

Overview & Synopsis

We consider the problem where a set of individuals has to classify m objects into p categories and does so by aggregating the individual classifications. We show that if m ≥ 3, m ≥ p ≥ 2, and classifications are fuzzy, that is, objects belong to a category to a certain degree, then an optimal and independent aggregator rule that satisfies a weak unanimity condition belongs to the family of Weighted Arithmetic Means. We also obtain characterization results for m = p = 2.