Continuous Classification Aggregation
This addresses a theoretical problem in social choice and aggregation theory for researchers in mathematics and economics, providing foundational results but is incremental as it extends known aggregation theorems to fuzzy classifications.
The paper proves that any optimal, independent, and zero unanimous fuzzy classification aggregation function for a continuum of individual classifications with at least three objects and two types must be a weighted arithmetic mean, and characterizes the case with exactly two objects and two types.
We prove that any optimal, independent, and zero unanimous fuzzy classification aggregation function of a continuum of individual classifications of $m\ge 3$ objects into $2\le p\le m$ types must be a weighted arithmetic mean. We also provide a characterization for the case when $m=p=2$.