I have a set of elements, {A,B,...Z}, and I can divide them into separate sub-sets. One way to divide the elements could be subdivision $\alpha$ so that {A,B}, {C,Z}, {D,E,F}, ... . A second way to divide the elements could be subdivision $\beta$ so that {A,C}, {Z}, {B,D,E,F}, ... ?
I would like a method to compare the different subdivisions of the sets that would return a number describing how similar they are. For instance, if the subdivisions are identical, the result is maximized. Then, the more that elements of subdivision $\beta$ are not grouped with the same elements as they are grouped with in subdivision $\alpha$, the lower the result.
Are there conventional methods for making this comparison? Can you help me find them?