Design and prediction of self-organizing interval type-2 fuzzy wavelet neural network.

• Based on the Euclidean distance between the input layer and the fuzzification layer, two sets of indicators are incorporated to assess the effectiveness and redundancy of current fuzzy rules. Rules determined as redundant are deleted. Meanwhile, new fuzzy rules are added when the current fuzzy rules become insufficient. Furthermore, a significance index is set to judge the essentiality of each fuzzy rule and remove unimportant rules. So that the algorithm can delete unimportant rules while deleting redundant rules. • The antecedent parameters of fuzzy rules are optimized by the AdaBound algorithm. By limiting the learning rate under a boundary value based on the Adam algorithm, this method has a higher training speed than the traditional gradient algorithm and simultaneously avoids the non-convergence caused by the extreme learning rate. • The adaptive gradient method is used to learn the consequences of fuzzy rules. By adjusting its learning rate with RMSE, this method can speed up the training speed while ensuring generalization capacity. • The proposed SIT2FWNN model is used to predict short-term traffic flow, Mackey-Glass chaotic time series, and the opening index of the Shanghai stock index and compared with similar studies. The simulation results demonstrate the superior network performance of the proposed SIT2FWNN in this paper. This paper presents a self-organizing interval type-2 fuzzy wavelet neural network (SIT2FWNN) model for predicting and identifying nonlinear systems. Based on traditional TSK interval type-2 fuzzy neural network (IT2FNN), the proposed SIT2FWNN utilizes the wavelet basis function with the locating abilities of time-domain and frequency-domain as the consequent of fuzzy rules, combining the capacity of IT2FNN to handle the uncertainty and the great learning potentiality of wavelet neural network (WNN). For the structural adjustment of SIT2FWNN, fuzzy rules are added and deleted according to the Euclidean distance between the input layer and the fuzzification layer. The self-organizing algorithm can delete redundant and unimportant fuzzy rules, thus optimizing the structure of SIT2FWNN and simplifying the calculation. In parameter learning, the AdaBound algorithm and self-adaptive gradient learning algorithm are used to find optimal values of unknown parameters of the SIT2FWNN model. Finally, the designed SIT2FWNN model is applied in the predictions of short-term traffic flow, Mackey-Glass time series, and the opening index of the Shanghai stock index. The evaluation comparison between the proposed model and similar studies proves that SIT2FWNN has higher prediction accuracy and speed. [ABSTRACT FROM AUTHOR]