Tversky index

sim_{Tversky}(x, y) = \frac{|x \cap y|}{|x \cap y| + \alpha |x \setminus y| + \beta |y \setminus x|}

Where:

$x \setminus y$ denotes the relative complement of $y$ in $x$ .
$\alpha, \beta \ge 0$ $α, β \geq 0$ are parameters of the Tversky index.
- $\alpha = \beta = 1$ produces the Jaccard index
- $\alpha = \beta = \frac{1}{2}$ produces the Dice coefficient

The Tversky index can be seen as a generalization of the Dice coefficient and the Jaccard index.

Reading