Fuzzy Classification Aggregation

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 $m\geq 3$, $m\geq p\geq 2$, 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 $m= p= 2$.