Self-Organizing Stacked Type-2 Fuzzy Neural Network With Rule Generalization

Type-2 fuzzy neural networks (T2FNNs) are particularly effective in dealing with nonlinear systems. However, they inevitably suffer from multicollinearity problems caused by the significant overlaps of the footprint uncertainty (FOU), which leads to generalization biases. To solve this challenge, a self-organizing stacked T2FNN with rule generalization (RG-SOST2FNN) is developed to boost its overall performance. First, a stacked technique with cosine smart priority is designed for T2FNN fusion. This technique employs multivariable cosine similarity to obtain sparse inputs, which selectively stacks multiple T2FNNs with non-collinear inputs to reduce collinearity dependence. Second, a dynamic stacked framework with a rule cluster generation mechanism is developed to achieve individual and batch rule adjustment. Then, a stacked structure with diversity is obtained to alleviate collinearity among rules by eliminating the singularity of the parameter matrix of FOUs. Third, a stacked risk mitigation algorithm is proposed to shape the fuzzy rule clusters (FRCs). Then, the parameters of FRCs are optimized using sparse gradient learning, which avoids the updating of collinear features to reduce the variance of parameter estimation. Finally, the simulation tests show that RG-SOST2FNN can achieve state-of-the-art performance even at high multicollinearity in complex systems.