Probabilistic approach to attributes coding in the rough sets theory

Objects in an information system analyzed by the rough sets theory methods are characterized by attributes, which can take on a finite set of values only. In diagnostic experiments, condition attributes are usually treated as continuous variables, taking values from certain intervals. So, to use this theory in such problems, certain discretization (coding) of continuous variables is needed. The optimal classification properties of an information system are taken by the authors as base criteria for selecting discretization. The concepts of a random information system and of an expected values of classification quality are introduced. As a result of discretization of continuous attributes, one can get a finite number of regions called states. It is observed that the optimal number of states is not greater than the number of objects