Search

This study presents an innovative approach to the design of a hybrid fuzzy classifier, with a focus on exploring the classification capability of a conventional fuzzy polynomial neural network (CFPNN). The proposed novel self-organizing hybrid fuzzy polynomial NN classifier (HFPNNC) improves performance while maintaining model interpretability and fixability by synergistically combining an adaptive network structure and the compound regularization technique (CRT). Recent studies have focused on exploring the potential of CFPNN structures for addressing regression issues. To effectively introduce the CFPNN framework to multiclassification tasks, a resilient fuzzy polynomial neural network structure was designed as a basic subclassifier to construct the proposed HFPNNC. The proposed HFPNNC employs a dynamically adaptive structure comprising of two types of critical layers: 1) the fuzzy set-based polynomial neurons layers and 2) the polynomial neurons layers. This allows the classifier to adapt to the complexity of classification tasks. To further strengthen the robustness and generalization ability of the HFPNNC, we incorporate the synergistic combination of probabilistic constrained competitive response selection (PCCRS) and ℓ2-norm regularization least squares estimation (ℓ2-LSE) methods to manage the generation of network layers and the estimation of neuron weights. As key constituents of the CRT approach, the PCCRS and ℓ2-LSE method strike a balance between model complexity and performance. The effectiveness of the proposed HFPNNC is thoroughly evaluated against classical classifiers, state-of-the-art fuzzy classifiers and deep learning baseline models using 17 public datasets, two real-world datasets, and three large-scale datasets. HFPNNC achieves the best prediction in 72.7% of the data. The experimental results and the statistical analysis show a remarkable advantage of the HFPNNC over existing methods, confirming its potential as a flexible, interpretable solution for classification tasks.

Time series forecasting is an essential and challenging task, especially for large-scale time-series (LSTS) forecasting, which plays a crucial role in many real-world applications. Due to the instability of time series data and the randomness (noise) of their characteristics, it is difficult for polynomial neural network (PNN) and its modifications to achieve accurate and stable time series prediction. In this study, we propose a novel structure of hierarchical neural networks (HNN) realized by long short-term memory (LSTM), two classes of self-organizing dynamical fuzzy neural network architectures of fuzzy rule-based polynomial neurons (FPNs) and polynomial neurons constructed by variant generation of nodes as well as layers of networks. The proposed HNN combines the deep learning method with the PNN method for the first time and extends it to time series prediction as a modification of PNN. LSTM extracts the temporal dependencies present in each time series and enables the model to learn its representation. FPNs are designed to capture the complex nonlinear patterns present in the data space by utilizing fuzzy C-means (FCM) clustering and least-square-error-based learning of polynomial functions. The self-organizing hierarchical network architecture generated by the Elitism-based Roulette Wheel Selection strategy ensures that candidate neurons exhibit sufficient fitting ability while enriching the diversity of heterogeneous neurons, addressing the issue of multicollinearity and providing opportunities to select better prediction neurons. In addition, L2-norm regularization is applied to mitigate the overfitting problem. Experiments are conducted on nine real-world LSTS datasets including three practical applications. The results show that the proposed model exhibits high prediction performance, outperforming many state-of-the-art models.

Fuzzy clustering-based neural networks (FCNNs) based on information granulation techniques have been shown to be effective Takagi–Sugeno (TS)-type fuzzy models. However, the existing FCNNs could not cope well with sequential learning tasks. In this study, we introduce incremental FCNNs (IFCNNs), which could dynamically update themselves whenever new learning data (e.g., single datum or block data) are incorporated into the dataset. Specifically, we employ dynamic (incremental) fuzzy C-means (FCMs) clustering algorithms to reveal a structure in data and divide the entire input space into several subregions. In the aforementioned partition, the dynamic FCM adaptively adjusts the position of its prototypes by using sequential data. Due to the time-sharing arrival of training data, compared with batch learning models, incremental learning methods may lose classification (prediction) accuracy. In order to tackle this challenge, we utilize quasi-fuzzy local models (QFLMs) based on modified Schmidt neural networks to replace the popular linear functions in TS-type fuzzy models to refine and enhance the ability to represent the behavior of fuzzy subspaces. Meanwhile, the recursive least square error (LSE) estimation is utilized to update the weights of QFLMs from one-by-one or block-by-block (fixed or varying block size) learning data. In addition, the $L_{2}$ regularization is considered to ameliorate the deterioration of generalization abilities caused by potential overfitting when carrying out weight estimation. The proposed method leads to the construction of FCNNs in a new way, which can effectively deal with incremental data as well as deliver sound generalization capability. Extensive machine-learning datasets and a real-world application are employed to show the validity and performance of the presented methods. From the experimental results, we show that the proposal can maintain sound classification accuracy when effectively processing sequential data.

Fuzzy min-max neural network (FMNN) is one kind of three-layer models based on hyperboxes that are constructed in a sequential way. Such a sequential mechanism inevitably leads to the input order and overlap region problem. In this study, we propose a deep FMNN (DFMNN) based on initialization and optimization operation to overcome these limitations. Initialization operation that can solve the input order problem is to design hyperboxes in a simultaneous way, and side parameters have been proposed to control the size of hyperboxes. Optimization operation that can eliminate overlap region problem is realized by means of deep layers, where the number of layers is immediately determined when the overlap among hyperboxes is eliminated. In the optimization process, each layer consists of three sections, namely, the partition section, combination section, and union section. The partition section aims to divide the hyperboxes into a nonoverlapping hyperbox set and an overlapping hyperbox set. The combination section eliminates the overlap problem of overlapping hyperbox set. The union section obtains the optimized hyperbox set in the current layer. DFMNN is evaluated based on a series of benchmark datasets. A comparative analysis illustrates that the proposed DFMNN model outperforms several models previously reported in the literature.