On multistage fuzzy neural network modeling

In the past couple of years, there has been increasing interest in the fusion of neural networks and fuzzy logic. Most of the existing fuzzy neural network (FNN) models have been proposed to implement different types of single-stage fuzzy reasoning mechanisms and inevitably they suffer from the dimensionality problem when dealing with complex real-world problems. To address the problem, FNN modeling based on multistage fuzzy reasoning (MSFR) is pursued here and two hierarchical network models, namely incremental type and aggregated type, are introduced. The new models called multistage FNN (MSFNN) model a hierarchical fuzzy rule set that allows the consequence of a rule passed to another as a fact through the intermediate variables. From the stipulated input-output data pairs, they can generate an appropriate fuzzy rule set through structure and parameter learning procedures proposed in this paper. In addition, we have particularly addressed the input selection problem of these two types of multistage network models and proposed two efficient methods for them. The effectiveness of the proposed MSFNN models in handling high-dimensional problems is demonstrated through various numerical simulations.