If the sizes of the rotted areas are relatively small you can cut out the rotted areas and put in a plywood patch that fits the hole. You can use strips of plywood underneath the joint between the patch and the rest of the floor. Go for something like 3 or 4 inches wide for the strips. Attach them to the main body of the floor with glue and decking screws from above. Clamps can help hold the strips in place while you put the screws in place. Attach the patch to the strips with glue and screws as well. You can fill the crack with something like Fixall and sand it to get an even surface for putting your flooring tiles back in. This techniques should work fine for fairly large areas too but your techniques would need to be a bit different around the edges of the floor. Are the places that need repair in the middle of the floor or are they at the edges?
If there is a lot more rot than expected you may have to do a full floor replacement which is, of course, a lot more work. Check out my posting #3 in the following thread for some more pointers to techniques I used for full floor replacement.
Hopefully you can get away with just localized patches.
I hope this helps,