Abstract
Rough set theory is a relative new tool that deals with vagueness and uncertainty inherent in decision making. This paper introduce a new probabilistic approach for reducing dimensions and extracting rules of information systems using expert systems. The core of the approach is a soft hybrid induction system called the Generalized Distribution Table and Rough Set System (GDT-RS) for discovering classification rules, Which is based on a combination of Generalized Distribution Table (GDT) and the Rough Set methodologies. The probabilistic properties of the Decision rules are discussed and the proposed probabilistic rough set approach was applied to discover grade rules of transformer evaluation when there is a missing failure symptom of transformer. The results show that the proposed approach represents explicitly the uncertainty of a rule, it can flexibly select biases for search control and it can effectively handle noisy and missing data.