Fourier-based type-2 fuzzy neural network: Simple and effective for high dimensional problems

The main contribution of this study is to introduce a simple and effective deep learning Fourier-based type-2 fuzzy neural network for high-dimensional problems. The rules are directly constructed by fast Fourier transformation. The input matrix/vector is segmented, and each segment represents a fuzzy rule. The upper/lower bounds of rule firings are obtained by the Fourier transformation approach. The output is computed by a simple type-reduction method. All antecedent and consequent parameters are opti-mized by simple gradient descent and fuzzy correntropy-based extended Kalman filter. The kernel size of a conventional correntropy-based filters is determined by a fuzzy system. The convergence of the learning method is proved by the Lyapunov method. The effectiveness of the suggested approach is ver-ified by the face recognition problem (1024 input variables), English handwriting digit recognition (1024 input variables), and modeling problem with real-world data set (32 input variables). The simulations and comparisons demonstrate the superiority of the introduced scheme.& COPY; 2023 Elsevier B.V. All rights reserved.