Assume I have two binary relations $R_{1}$ and $R_{2}$ on a set $S$, i.e., two subsets of $S \times S$. I want to compare these two relations in terms of similarity. Is there any distance metric that I can apply? The two relations are both complete, reflexive, antisymmetric and transitive. Alternatively, we could assume that both relations are irreflexive, asymmetric, transitive, and $a \neq b \Longrightarrow aRb \lor bRa$.
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1Perhaps you may check the Hamming metric. – Anton Vrdoljak Dec 01 '23 at 08:00
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Thank you, Anton. That would be the number of elements that are in one set but not in the other. Not perfectly adjusted for the problem at hand, but something to start with. – Florian Dec 01 '23 at 14:27
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You're welcome @Florian! – Anton Vrdoljak Dec 01 '23 at 17:47