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 first a parametrized family of concept approximations is built and next, by parameters tuning the best, in a sense, approximation is chosen (see e.g. the variable precision rough set model [40]). 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. Elements of approximation space are parametrized, moreover for the proper application of such model to a particular data set it is necessary to make optimization of the parameters. We discuss not only basic properties of the mentioned model, but strategies of parameters optimization as well. We also present different notions of rough relations. Optimization of different parameters can be based on the degree of inclusion of relations defined by condition and decision attributes. Some illustration of presented methods on real life medical data set is also included.