A refined classification method with tolerance relation-based rough sets for incomplete decision systems

Generally, the sample data of Multiple Attributes Decision Making (MADM) problems is incomplete because of variety of factors such as noise in data, compactness of representation, prediction capability and randomness of experiment. Rough set theory is a useful mathematical tool for this incomplete decision systems, while the fuzziness of relation-based classification and uncertainty of attribute reduction always exist in traditional extended rough sets model. In order to classify the incomplete decision systems effectively, a new refined classification method with tolerance relation-based rough sets was presented in this paper. Considering the randomness of missing value, this method used attribute importance to replace attribute reduction to establish refined classification rules directly. Not only it can reduce the computational complexity, but also can increase classification accuracy. From the analysis and comparison of examples about classification problems of air weapon targets, the effectiveness and stability of this method for incomplete decision systems were verified.