Structural learning of RBF-fuzzy rule bases based on information criteria and degeneration

There are some difficulties in researches on supervised learning using fuzzy rule-based systems: the difficulty of selecting effective input variables and the difficulty of selecting a proper rule structure. To solve these difficulties, we proposed GA^d (Genetic Algorithm with Degeneration), which performs structural learning. It is thought that if the information criteria of systems can be optimized, the obtained systems become more general, or can explain unlearned data better. But when GA^d optimizes the information criteria directly, there are some cases when too many parameters will be lost in earlier generations. In this study, the idea of multi-objective optimization, in which estimation errors and information criteria are both optimized, is introduced to avoid this problem. The weight for the errors is bigger in earlier generations and the weight for the information criteria becomes bigger in later generations. It is shown that this idea is effective to the structural learning of RBF fuzzy rule-based systems.