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arXiv · 2507.05919

Axiomatic characterizations of dissimilarity orderings and distances between sets

Thierry Marchant·Sandip Sarkar
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Abstract

We axiomatically characterize the orderings of pairs of sets induced by several distances: Hamming, Jaccard, S{\o}rensen-Dice and Overlap. We also axiomatically characterize these distances. Our axioms are properties describing how a distance changes when we perform elementary modifications of the sets, like adding one element to one of the sets, to both sets, swapping both sets, permuting some elements, etc.

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Thierry Marchant, Sandip Sarkar. 2025-07-08. Axiomatic characterizations of dissimilarity orderings and distances between sets. https://arxiv.org/abs/2507.05919

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