Correctness of a set with respect to another set.

Question

Is there a specific measure for correctness of a Set w.r.t another set? e.g. Consider there's a base set A, and a set B whose correctness needs to be measured w.r.t set A. Now B might contain some additional elements w.r.t A, and/or might be missing a few elements. Is there a well defined and widely accepted measure for correctness of set B w.r.t set A?

Answer 1

So $B$ is supposed to contain just the elements of $A$. $A, B \subset S$.

Let $FP$ (for false positives) $= |B \setminus A|$.

Let $FN$ (for false negatives) $= |A \setminus B|$.

Let $TP = |A \cap B|$.

Let $TN = |(S \setminus A) \cap (S \setminus B)|$

Then a measure might be $TP \times v_{TP} + TN \times v_{TN} - FN \times c_{FN} - FP \times c_{FP}$ where $v_{TP}$ is value of true positive and $c_{FN}$ is cost of false negative.