A efficiency complete algorithm for attribute reduction

A complete algorithm for attribute reduction in rough set theory based on discernibility matrix was introduced. This algorithm was composed of algorithm1 and algorithm2. Algorithm1 is to select those important condition attributes based on attribute frequency function in every iteration. Algorithm2 removes redundancy and incompatibility attributes in R found out by algorithm1. The time complexity of the algorithms in the worst case was analyzed and the proof of its completeness was given. Algorithm1 and algorithm2 guarantee that the reduction is probable a smallest or smaller one.