Continuous Classification Aggregation

TL;DR

This paper characterizes the form of optimal fuzzy classification aggregation functions, showing they are weighted arithmetic means for multiple objects and providing specific results for the case of two objects and types.

Contribution

It provides a mathematical proof that optimal aggregation functions are weighted arithmetic means for multiple objects and characterizes the case when there are two objects and types.

Findings

Optimal aggregation functions are weighted arithmetic means for multiple objects.

Characterization of the case with two objects and two types.

Mathematical proof of the form of aggregation functions.

Abstract

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 $m=p=2$.