Attribute reduction with fuzzy rough self-information measures

The fuzzy rough set is one of the most effective methods for dealing with the fuzziness and uncertainty of data. However, in most cases this model only considers the information provided by the lower approximation of a decision when it is used to attribute reduction. In a realistic environment, the uncertainty of information is related to lower approximation as well as upper approximation. In this study, we construct four kinds of uncertainty measures by combining fuzzy rough approximations with the concept of self-information. These uncertainty measures can be employed to evaluate the classification ability of attribute subsets. The relationships between these measures are discussed in detail. It is proven that the fourth measure, called relative decision self-information, is better for attribute reduction than the other measures because it considers both the lower and upper approximations of a fuzzy decision. The proposed measures are generalizations of classical measures based on fuzzy rough sets. Finally, we have designed a greedy algorithm for attribute reduction. We validate the effectiveness of the proposed method by comparing the experimental results for efficiency and accuracy with those of three other algorithms using fundamental data.