A novel reinforced dual-flow neural network based on attention and a polynomial-based radial basis function network (DFBTP) is proposed to enhance classification performance on tabular data. DFBTP consists of two types of architectures such as advanced Transformer model based on Tabular Prior data Fitted Network (TabPFN) and SV-clustering driven radial basis function neural network (SV-PRBFNN). The conventional PRBFNN model may encounter local minima and noise issues during training, which negatively impacts its performance. Local minima result from initial parameter choices, and noise issues are inherent in the dataset. By introducing the Transformer model and the Whale Optimization Algorithm (WOA), these challenges can be mitigated. Within the dual-flow architecture, the attention flow is trained using Bayesian inference capabilities and structural causal models, and it uses the self-attention mechanism to capture global features. This approach mitigates the problem of local minima. SV-PRBFNN flow uses the fuzzy clustering algorithm based on support vectors to replace the original radial basis function for training. Fuzzy clustering based on support vectors can alleviate the negative impact of outliers on model performance and also reduce the number of fuzzy rules. During neural network hyperparameter optimization, WOA is used to identify the global optimal values for hyperparameters. In the experiments, DFBTP demonstrated its superiority in classification accuracy in comparative experiments on 18 datasets and 13 models, and also performed well on real-world datasets. The robust performance of DFBTP was further validated through statistical analysis of the experimental results.

In the era of digital transformation, the large-scale deployment of sensors has led to the collection of highly complex and diverse data, posing significant challenges for multivariate time series forecasting (MTSF). Traditional forecasting approaches, often based on linear assumptions, are limited in their ability to capture the nonlinear temporal dynamics prevalent in real-world scenarios. To address these challenges, this study proposes an innovative multivariate prediction framework that integrates deep learning with traditional machine learning techniques. The framework incorporates an asymmetric transfer entropy coefficient (ATC) to identify genuine causal relationships among features, constructing a directed graph for feature importance ranking. This mechanism enhances feature selection by capturing both dynamic and static relationships among variables. An enhanced fuzzy C-means clustering algorithm, SCFCM, is introduced, which incorporates cosine similarity and Euclidean distance to improve sample discriminability in high-dimensional spaces and enhance clustering accuracy. Bayesian optimization is employed to dynamically determine the kernel sizes and numbers of the CNN-Transformer (Convolutional neural network-Transformer) prediction network, thereby improving feature extraction efficiency. The unified architecture integrates feature selection, clustering, and forecasting, achieving superior predictive performance. This comprehensive prediction model is referred to as ATC-SCFCM-DKCNT. Experiments on six real-world datasets demonstrate that ATC-SCFCM-DKCNT consistently outperforms state-of-the-art methods in terms of prediction accuracy and computational efficiency, highlighting its strong generalization ability and robustness in handling complex, high-dimensional data.

In this article, a novel attention-based reinforced interval type-2 fuzzy clustering neural network (ARIT2FCN) is developed to improve the generalization performance of fuzzy clustering-based neural networks (FCNNs). Commonly, fuzzy rules in FCNNs are generated through the clustering-based rule generator. However, the generated fuzzy rules may not be able to fully describe the given data, because the clustering-based rule generator does not simultaneously consider the intracluster homogeneity and intercluster heterogeneity for both of data characteristics and label information when defining membership functions (MFs) of fuzzy rules. This negatively affects fuzzy rules to accurately quantify the interclass heterogeneity and intraclass homogeneity and degrades the performance of FCNNs. The ARIT2FCN is proposed with the aid of the attention-based clustering mechanism and the successive learning method. The attention-based clustering mechanism is designed to define MFs by simultaneously considering data characteristics and label information. The successive learning method is adopted to construct the desired fuzzy rules that can capture the interclass heterogeneity and intraclass homogeneity. Moreover,L$_{2}$norm regularization is used to alleviate the overfitting effect. The performance of ARIT2FCN is evaluated on machine learning datasets with 16 comparative methods. In addition, two real-world problems are adopted to validate the effectiveness of ARIT2FCN. Experimental results demonstrate that the ARIT2FCN outperforms the comparative methods, and the statistical tests also support the superiority of ARIT2FCN.

In this article, we present a dimensionality reduction methodology of reinforced fuzzy-rule-based neural networks (FRNNs) realized with the help of determination/correlation coefficient-based streamlined feature selection strategy and fuzzy clustering with standard deviation to cope with high-dimensional data. This approach aims to reduce the design process of the proposed networks and to curb the computational overhead inherently associated with the increasing volume of data both in terms of their number and the dimensionality of the feature space. The overall architecture and learning mechanism of the FRNNs are based on radial basis function neural networks. However, we design the hidden layer of RBFNNs differently by using fuzzy clustering, which makes it easy to determine the parameters, such as centers and widths of the receptive fields (activation functions). Unlike conventional neural networks, the RBFNNs do not have a feature to support dimensionality reduction. To overcome this limitation, FRNNs select input variables by evaluating the adjusted determination coefficient of the model. To reduce the computational burden of finding an appropriate combination of inputs, we propose a simplified feature selection and elimination technique, in which the variables are selected or eliminated by correlation coefficients. A linear function expresses the connection weight, and we apply L2-norm regularization to least-square-error-based learning to estimate stable coefficients (weights), which is expected to significantly improve the generalization ability. The superiority of the proposed FRNNs was demonstrated by using 28 real-world benchmark datasets. The networks are also compared with the conventional models associated with the FRNNs and several related models previously published in the literature.

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 (FPN) and polynomial neurons (PN) 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 non-linear patterns present in the data space by utilizing Fuzzy C-Means clustering (FCM) and least square error (LSE)-based learning of polynomial functions. The self-organizing hierarchical network architecture generated by the Elitism-based Roulette Wheel Selection (ERWS) 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 9 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.

This paper studies the high complexity of the calculation of fuzzy measures which can be used in fuzzy integrals to combine the decisions of different learning algorithms. To this end, this paper proposes an alternative low complexity method for the calculation of fuzzy measures that have been applied to Choquet integral for the fusion of deep learning models across different application domains for increasing the accuracy of the overall model. The paper shows that the Dempster-Shafer (DS) belief structure provides partial information about the fuzzy measures associated with a variable, and the paper devises a method to use this partial information for the calculation of fuzzy measures. An infinite number of fuzzy measures is associated with the DS belief structure. This paper proposes a theorem to calculate the general form of a specific set of fuzzy measures associated with the DS belief structure. This specific set of fuzzy measures can be expressed as a weighted summation of the basic assignment function of the DS belief structure. The main advantage of expressing the fuzzy measures in this format is that the monotonic condition which needs to be maintained during the calculation of the fuzzy measure can be avoided and only the basic assignment function needs to be evaluated. The calculation of the basic assignment function is formulated using a method inspired by the Monte Carlo approach used to calculate Value Functions in Markov Decision Process.

Under the present circumstances, when we are still under the threat of different strains of coronavirus, and since the most widely used method for COVID-19 detection, RT-PCR is a tedious and time-consuming manual procedure with poor precision, the application of Artificial Intelligence (AI) and Computer-Aided Diagnosis (CAD) is inevitable. Though, some vaccines have now been authorized worldwide, it will take huge time to reach everyone, especially in developing countries. In this work, we have analyzed Chest X-ray (CXR) images for the detection of the coronavirus. The primary agenda of this proposed research study is to leverage the classification performance of the deep learning models using ensemble learning. Many papers have proposed different ensemble learning techniques in this field, some methods using aggregation functions like Weighted Arithmetic Mean (WAM) among others. However, none of these methods take into consideration the decisions that subsets of the classifiers take. In this paper, we have applied Choquet integral for ensemble and propose a novel method for the evaluation of fuzzy measures using coalition game theory, information theory, and Lambda fuzzy approximation. Three different sets of fuzzy measures are calculated using three different weighting schemes along with information theory and coalition game theory. Using these three sets of fuzzy measures, three Choquet integrals are calculated and their decisions are finally combined. Besides, we have created a database by combining several image repositories developed recently. Impressive results on the newly developed dataset and the challenging COVIDx dataset support the efficacy and robustness of the proposed method. Our experimental results outperform many recently proposed methods.

Regression Analysis is an analyzing method of regression model to explain the statistical relationship between explanatory variables and response variables. This paper propose a new regression analysis applying Theil's method based on F-transform. The main advantage of Theil's method in regression is the robustness, which means that it is not sensitive to outliers. The proposed method uses the median of rates of increments which are obtained from F-transform, based all possible pairs of F-transformed data in order to estimate the coefficients of fuzzy regression model. An example is given to show that the proposed regression analysis applying Theil's method based on F-transform is more robust than the least squares estimation (LSE) and even more robust than the original Theil's method.

A new modified Fuzzy transform (F-transform) method which is combined with the bootstrap technique for forecasting is proposed in this paper. We apply the bootstrap technique to improve the accuracy of the F-transform method. An example is given to show the superior of proposed method.