Belief rule-based system with two-stage optimization approach for handling class-imbalance problems

Class imbalance is a common problem in the real world and has significant impacts on rule-based systems (RBSs). Although many data-level and algorithm-level methods have been proposed, they are usually trapped in the dilemmas: (1) how to determine the number of parameters and their optimal value for a RBS automatically; and (2) how to provide an ad hoc solution for the RBS to enable its ability in handling class-imbalance problems. This study focuses on a promising RBS, namely belief RBS (BRBS), and proposes a two-stage optimization modeling approach to address both dilemmas simultaneously. The first stage performs structure optimization and rule distribution calibration, while the second stage conducts parameter optimization guided by imbalance measurement. Owing to the above two-stage optimization modeling, multiple balanced belief rule-bases (BRBs) can be automatically constructed using imbalanced data to form an effective BRBS. In order to verify the effectiveness of the proposed BRBS, one real class-imbalance dataset regarding lymph node diagnosis and five benchmark class-imbalance datasets are used to conduct a series of comparative experiments. The results demonstrate that the proposed BRBS performs better than some data sampling methods and class-imbalance classifiers.