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 optimized 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 verified 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.