Axiomatic characterizations of dissimilarity orderings and distances between sets

TL;DR

This paper provides axiomatic characterizations of how various set distances and their induced orderings behave, including Hamming, Jaccard, Sørensen-Dice, and Overlap, enhancing understanding of their properties.

Contribution

It offers the first axiomatic characterizations of these set distances and the orderings they induce, clarifying their foundational properties.

Findings

Characterization of set distance orderings

Axiomatic foundations for Hamming, Jaccard, Sørensen-Dice, Overlap

Insights into the properties of these distances

Abstract

We characterize the orderings of pairs of sets induced by several distances: Hamming, Jaccard, S\o rensen-Dice and Overlap. We also characterize these distances.