Abstract: Compared to extracting rules from complete data, it is more difficult to do that from incomplete data in fault diagnosis. A method that can directly extract the optimal generalized decision rules for fault diagnosis from incomplete data based on the rough set is proposed. The definition of discernibility matrix primitive is presented, and its property is investigated to simplify the computing course. According to the definition of discernibility matrix primitive, the definition of object-oriented discernibility matrix in the incomplete decision table for fault diagnosis is also presented. Using these concepts to construct the object-oriented discernibility function, with the basic equivalent forms in propositional logic such as distributive laws and absorption rate, the method that computes the minimal reductions of object-oriented is proposed, which implements the computation of object-oriented reductions in the incomplete decision rules for fault diagnosis and the extraction of the optimal generalized decision rules for fault diagnosis. Combined with a fault diagnosis example of operational state of an electric system, the application approach of the method is presented. And the validity of this method is proved.

Key words: Discernibility matrix primitive, Fault diagnosis, Incomplete data, Rough set, Rule extraction