Compact Rule Learner on Weighted Fuzzy Approximation Spaces for Class Imbalanced and Hybrid Data

Rough set theory is an efficient tool for machine learning and knowledge acquisition. By introducing weightiness into a fuzzy approximation space, a new rule induction algorithm is proposed, which combines three types of uncertainty: weightiness, fuzziness and roughness. We first define the key concepts of block, minimal complex and local covering in a weighted fuzzy approximation space, then a weighted fuzzy approximation space based rule learner, and finally a weighted certainty factor for evaluating fuzzy classification rules. The time complexity of proposed rule learner is theoretically analyzed. Furthermore, in order to estimate the performance of the proposed method on class imbalanced and hybrid datasets, we compare our method with classical methods by conducting experiments on fifteen datasets. Comparative studies indicate that rule sets extracted by this method get a better performance on minority class than other approaches. It is therefore concluded that the proposed rule learner is an effective method for class imbalanced and hybrid data learning.