Approximating functions using rough sets

Approximating of functions that are specified using imperfect knowledge is one of the central issues of many areas such as machine learning, pattern recognition, data mining, or qualitative reasoning. However, we do not have yet satisfactory methods for approximation of functions and developed calculi on function approximations. In the paper we discuss a function approximation using the rough set approach. The main difference with the existing approaches in rough set theory is based on modification of the inclusion measure. This makes it possible to overcome some drawbacks of the previously used definitions. For applications it is important to develop rough measures on approximated objects, in particular on function approximations. The modified inclusion measure is also used to define an exemplary measure, i.e., the rough integral.