I have an application where I have a number of sets. A set might be
{4, 7, 12, 18}
unique numbers and all less than 50.
I then have several data items:
1 {1,
I see another solution which is dual to yours (i.e., testing a data item against every set) and that is using a binary tree where each node tests whether a specific item is included or not.
For instance if you had the sets A = { 2, 3 } and B = { 4 } and C = { 1, 3 } you'd have the following tree
_NOT_HAVE_[1]___HAVE____
| |
_____[2]_____ _____[2]_____
| | | |
__[3]__ __[3]__ __[3]__ __[3]__
| | | | | | | |
[4] [4] [4] [4] [4] [4] [4] [4]
/ \ / \ / \ / \ / \ / \ / \ / \
. B . B . B . B B C B A A A A
C B C B
C
After making the tree, you'd simply need to make 50 comparisons---or how ever many items you can have in a set.
For instance, for { 1, 4 }, you branch through the tree : right (the set has 1), left (doesn't have 2), left, right, and you get [ B ], meaning only set B is included in { 1, 4 }.
This is basically called a "Binary Decision Diagram". If you are offended by the redundancy in the nodes (as you should be, because 2^50 is a lot of nodes...) then you should consider the reduced form, which is called a "Reduced, Ordered Binary Decision Diagram" and is a commonly used data-structure. In this version, nodes are merged when they are redundant, and you no longer have a binary tree, but a directed acyclic graph.
The Wikipedia page on ROBBDs can provide you with more information, as well as links to libraries which implement this data-structure for various languages.