Organized grouping

Kind of a strange problem so I'm not sure if anyone will have any input but I figured it's worth a shot.

I am trying to automate (or at least ease) the organization of several user permissions into user "classes" from an automatically generated report. There are approximately 95 different permissions belonging to different applications and an employee can have any number of these permissions (though, realistically, the most that anyone will have will be around 15). I would like to setup user classes which are just logical groupings of permissions (not necessarily based on application).

My main problems are that user classes don't have to be mutually exclusive and a user can have multiple userclasses to make reflect the permissions he has. I'd like a set of the minimum number of groups (with the max number of permissions in each group) that would be able to accurately reflect everyone's permissions.

I'm not sure if I've explained everything clearly enough so if anyone would like to assist and needs more info please let me know. I'm thinking that if I had decided not to skip over Set Theory class back in college I'd probably have a better grasp of this problem.

Any input would be greatly appreciated in the form of specific examples or key words that I should be searching for on google. BTW, this is in PHP and should be only a 1 time data merge so the algorithm doesn't necessarily need to be the quickest or most efficient.
TIA
-b

Before I think too hard to work out a wrong solution or anything, lets get this straight...

you want a minimum number of sets, each one of which contains a number of permissions, and each user can belong to one or more sets??

From this you need to be able to create any user 'class', i.e. a user with any set of permissions from this??

Which operations will be allowed, just the union of the sets, or can intersection be allowed also?

Let me know and I'll see if I can help at all...

Thx, for the offer, already solved my problem with another approach, but yeah your assessment was right with union and intersection allowed.

Thanks again.
-b