Rough Sets and Rule Induction in Imperfect Information Systems

The original rough set theory deals with precise and complete data, while real applications frequently contain imperfect information. A typical imperfect data studied in rough set research is the missing values. Though there are many ideas proposed to solve the issue in the literature, the paper adopts a probabilistic approach, because it can incorporate other types of imperfect data including imprecise and uncertain values in a single approach. The paper first discusses probabilities of attribute values assuming different type of attributes in real applications, and proposes a generalized method of probability of matching. This probability is then used to define valued tolerance/similarity relations and to develop new rough set models based on the valued tolerance/similarity relations. An algorithm for deriving decision rules based on the rough set models is also studied and proposed.