Optimizations of Rough Set Model

Rough set methodology is based on concept (set) approximations constructed from available background knowledge represented in information systems 14]. In many applications only partial knowledge about approximated concepts is given. Hence quite often rst a parametrized family of concept approximations is built and next by tuning of the parameters the best, in a sense, approximation is chosen (see e.g. variable precision rough set model 40]) in approximation spaces. In this paper we follow this approach in generalized approximation spaces. We discuss rough set model based on approximation spaces with uncertainty functions and rough inclusions. Both elements of approximation space are parametrized and for the proper application of such model to a particular data set it is necessary to make optimization of the parameters. We discuss basic properties of the mentioned model and also strategies of parameters optimization. We also present diierent notions of rough relations. Optimization of diierent parameters can be based on degree of inclusion of relations deened by condition and decision attributes. Some illustration of presented methods on real medical data set is also included.