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.