Abstract
The concept of the complement of a covering is introduced, and then the extended space of a covering approximation space is induced based on it. Generally, the extended space of a covering approximation space generates a bigger covering lower approximation or smaller covering upper approximation than itself. Through extending each covering of a covering decision system, the classification ability of each covering may be improved. Thus, a heuristic reduction algorithm is developed to eliminate some coverings in a covering decision system without decreasing the classification ability of the system for decision. Theoretical analysis and experimental results indicate that this algorithm can often get smaller reduction than other algorithms.