In order to resolve the error of computing core and attribute reduction, which was caused by the inconsistency of decision table, a definition of object credibility was introduced and added into the decision table to tell inconsistent objects and consistent objects. Then a definition of discernibility matrix and definitions of core and attribute reduction based on the discernibility matrix were put forward. It was proved that the core and attribute reduction acquired from the definitions are the core and attribute reduction based on positive region. Finally, the general algorithm and its improved algorithm for computing attribute reduction were designed, and both of example and experiment results showed that the algorithms are effective.
