# Rough Set Approach

We can use the rough set approach to discover structural relationship within imprecise and noisy data.

**Note** − This approach can only be applied on discrete-valued attributes. Therefore, continuous-valued attributes must be discretized before its use.

The Rough Set Theory is based on the establishment of equivalence classes within the given training data. The tuples that forms the equivalence class are indiscernible. It means the samples are identical with respect to the attributes describing the data.

There are some classes in the given real world data, which cannot be distinguished in terms of available attributes. We can use the rough sets to**roughly** define such classes.

For a given class C, the rough set definition is approximated by two sets as follows −

**Lower Approximation of C**− The lower approximation of C consists of all the data tuples, that based on the knowledge of the attribute, are certain to belong to class C.**Upper Approximation of C**− The upper approximation of C consists of all the tuples, that based on the knowledge of attributes, cannot be described as not belonging to C.

The following diagram shows the Upper and Lower Approximation of class C: