The basic idea behind rough sets is that while some cases may be clearly labeled as being in a set X (the "positive region"), and some cases may be clearly labeled as not being in set X (the "negative region"), limited information prevents us from labeling all possible cases clearly. The remaining cases, cannot be distinguished and lie in what is known as the "boundary region". Rough sets theory calls the positive region a "lower approximation" of set X, which yields no false positives. The positive region plus the boundary region make up an "upper approximation" of set X, which yields no false negatives. The practical end of rough sets theory deals with binning continuous inputs and deciding which areas of the input space should be included in these various approximations.

*last updated:* 17 March 2008