In this paper, a new de-fuzzification algorithm is proposed for multi-classification problems, which can effectively improve the accuracy, stability and computational efficiency of interval type-2 fuzzy systems. In addition, in order to enable the fuzzy system to handle high-dimensional data, this paper also designs a collaborative feature selection strategy based on gate function and GroupL0regularisation, which effectively solves the challenges faced by fuzzy systems when dealing with high-dimensional problems. The strategy allows the system to select relevant features and alleviate the curse of dimensionality. Finally, we employ a Root Mean Square Propagation algorithm to simultaneously optimise the antecedent and consequent parameters in the interval type-2 TSK (Takagi-Sugeno-Kang) fuzzy system, and conduct a convergence analysis of the algorithm to ensure the validity and reliability of the proposed method. To verify the performance of the proposed algorithm, we conducted simulation experiments on high-dimensional datasets. The results demonstrate the superiority of our method in handling multiclassification tasks and the ability to handle complex highdimensional data.

In recent years, bidirectional convolutional recurrent neural networks (RNNs) have made significant breakthroughs in addressing a wide range of challenging problems related to time series and prediction applications. However, the performance of the models is highly dependent on the hyperparameters chosen. Hence, we propose an automatic method for hyperparameter optimization and apply a bidirectional convolutional RNN based on the improved swarm intelligence optimization (sparrow search) to solve regression prediction problems. Specifically, a parallel multiscale dilated convolution (PMDC) module was designed to capture both local and global spatial correlations. This method utilizes convolution with different dilation rates to expand the receptive field without increasing the complexity of the model. Meanwhile, it integrates parallel multiscale structures to extract features at different scales and enhance the model's understanding of the input data. Then, the bidirectional gated recurrent units (BGRUs) learn temporal information from the convolutional features. To address the limitations of empirical hyperparameter selection, such as slow training and low efficiency, a novel PMDC-BGRU model integrated with a pretrained sparrow search algorithm (SSA) was proposed for hyperparameter optimization. Finally, experiments on multiple datasets verified the superiority of the algorithm and explained the flexibility of intelligent optimization algorithms in solving model parameter optimization.

Recurrent neural networks (RNNs) have been found to be a promising field of research for time series prediction, continuous-time system modeling, and discrete-time sequence data processing. The Elman network can be viewed as an RNN with a single layer of feedback connections and local storage units. However, the Elman network has two limitations that restrict its application. One is the overfitting phenomenon, which limits its generalization ability. The other is the complexity of the network structure, which makes its theoretical results incomplete and limits its practicality. The main contribution of this article is to propose a new Elman network model with a regularization term. First, we demonstrate the convergence of the backpropagation algorithm with weight decay regularization under some reasonable conditions. Second, contrary to the usual requirement for bounded weights, we show that such boundedness is no longer a necessary condition for convergence analysis. Third, we show that the requirements for learning rate and the stable set of error functions can also be relaxed. Finally, we provide simulation results to demonstrate the excellent performance of our proposed algorithm.

In this article, we investigate the boundedness and convergence of the online gradient method with the smoothing group regularization for the sigma-pi-sigma neural network (SPSNN). This enhances the sparseness of the network and improves its generalization ability. For the original group regularization, the error function is nonconvex and nonsmooth, which can cause oscillation of the error function. To ameliorate this drawback, we propose a simple and effective smoothing technique, which can effectively eliminate the deficiency of the original group regularization. The group regularization effectively optimizes the network structure from two aspects redundant hidden nodes tending to zero and redundant weights of surviving hidden nodes in the network tending to zero. This article shows the strong and weak convergence results for the proposed method and proves the boundedness of weights. Experiment results clearly demonstrate the capability of the proposed method and the effectiveness of redundancy control. The simulation results are observed to support the theoretical results.

Compared with traditional learning methods such as the back propagation (BP) method, extreme learning machine provides much faster learning speed and needs less human intervention, and thus has been widely used. In this paper we combine the L 1/2 regularization method with extreme learning machine to prune extreme learning machine. A variable learning coefficient is employed to prevent too large a learning increment. A numerical experiment demonstrates that a network pruned L 1/2 regularization has fewer hidden nodes but provides better performance than both the original network and the network pruned by L 2 regularization.