In this paper, we propose a hybrid ensemble polynomial neural network (HEPNN) with the aid of polynomial neural network (PNN) and hybrid ensemble polynomials neurons (HEPNs). Two types of HEPNs including ensemble radial-based-function polynomial neuron (ERPN) and ensemble polynomial neuron (EPN) are proposed. ERPN and EPN are generalized polynomial neurons based on ensemble architecture. To address the problem of multiple covariance in traditional PNN neural networks, correlation coefficients and performance are utilized to select neurons replacing the original selection of nodes by performance only. The main strategies of HEPNN design are as follows: First, the first layer of the network consists of ERPN that are utilized to reflect the structure encountered between the data, while the second and higher layers consists of EPN, which reflect higher polynomial-order relationships between input and output data. Second, particle swarm optimization (PSO) is adopted to optimize the architecture of HEPNN. A comparative study shows the proposed HEPNN has better performance than other state-of-art models reported in literature.

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.

In this article, we propose the concept of random polynomial neural networks (RPNNs) realized based on the architecture of polynomial neural networks (PNNs) with random polynomial neurons (RPNs). RPNs exhibit generalized polynomial neurons (PNs) based on random forest (RF) architecture. In the design of RPNs, the target variables are no longer directly used in conventional decision trees, and the polynomial of these target variables is exploited here to determine the average prediction. Unlike the conventional performance index used in the selection of PNs, the correlation coefficient is adopted here to select the RPNs of each layer. When compared with the conventional PNs used in PNNs, the proposed RPNs exhibit the following advantages: first, RPNs are insensitive to outliers; second, RPNs can obtain the importance of each input variable after training; third, RPNs can alleviate the overfitting problem with the use of an RF structure. The overall nonlinearity of a complex system is captured by means of PNNs. Moreover, particle swarm optimization (PSO) is exploited to optimize the parameters when constructing RPNNs. The RPNNs take advantage of both RF and PNNs: it exhibits high accuracy based on ensemble learning used in the RF and is beneficial to describe high-order nonlinear relations between input and output variables stemming from PNNs. Experimental results based on a series of well-known modeling benchmarks illustrate that the proposed RPNNs outperform other state-of-the-art models reported in the literature.

The minimum path pair (MPP) query problem is to find the optimal meeting point of two minimum paths for two users in a network, where each user's minimum path has its own departure and destination nodes. However, the MPP query problem on a time-varying network that generally exists in the world remains open. In this study, we investigate the time-varying minimum path pair (TMPP) query problem, where the arcs of the network are time dependent. We first model the TMPP and then propose a time impulse neural network (TINN) to solve the TMPP. In the design of the TINN, the entire network topology is considered as the architecture of the neural network, and each node is viewed as a neuron. The core of an impulse-based neuron consists of six parts: input, impulse receiver, time window selector, neuron storage, impulse sender, and output. Unlike the traditional neural network, the whole neural network does not require a training process but is implemented through an impulse mechanism. The TINN consists of two stages; the first stage is to find the two minimum paths of two users, while the second stage is to calculate the distance between these two minimum paths. The underlying idea of the TINN is to find the minimum path using an impulse mechanism. The minimum path relies on the earliest time impulse stemming from the depart node that arrives at the destination node. With this mechanism, both the minimum path of the network and the distance between two paths can be addressed. Furthermore, theoretical analysis demonstrates the correctness and provides the complexity of the TINN. Experiments of the TINN are carried out based on the well-known New York City Map. A comparative study illustrates the effectiveness of the TINN.

Atrial fibrillation detection (AFD) has attracted much attention in the field of embedded systems. In this study, we propose a sorting fuzzy min-max (SFMM) model, and then develop an SFMM-based embedded system for AF detection. The proposed SFMM model is essentially enhanced the fuzzy min-max (FMM) model that have been successfully applied in many classification fields. In comparison with the typical FMM model, the proposed SFMM model can overcome the limitation of the input order problem encountered in the typical FMM model. The embedded system consists of a control chip and an analog-digital conversion (ADC) chip. The STM32F407 chip is used as the control chip and the ADS1292 chip, which has a high common-mode rejection ratio (CMRR), is used as the ADC chip. A series of machine learning benchmarks are included to evaluate the performance of the SFMM model. Experimental results on AF data further demonstrate the effectiveness of the SFMM-based embedded system.

Traditional image classification methods mostly use offline learning mode, which takes a lot of time when data is updated. In this paper, we propose a density-sorting-based convolutional fuzzy min-max neural network (DCFMNN) for image classification to solve this problem. DCFMNN is realized based on convolutional Neural Network (CNN) and density-sorting-based fuzzy min-max neural network. CNN is applied for image feature extraction. Density-sorting-based fuzzy min-max neural network is used for classification, which includes density-based sorting part and fuzzy min-max (FMM) neural network part. In the part of density-based sorting, patterns are sorted according to the points with the highest density in the same class and two densest points are considered for selection. The purpose is to overcome the influence of the pattern input order in the original FMM on the creation of the hyperbox. In the part of FMM, the fuzzy set classification method is used to enable online learning. Diverse CNN architectures are applied to DCFMNN. The benchmark image datasets were employed for evaluation on DCFMNN. Experimental results show that DCFMNN has high classification accuracy and less network complexity, and its online learning ability reduces the training time.

The classical fuzzy min-max (FMM) neural network easy to cause the overlap of hyperboxes from different classes, which affect the pattern classification performance. In this paper, we propose a redefined fuzzy min-max (RFMM) neural network to solve this problem. The main contribution is to modify the basic architecture of FMM by adding a redefined hyperbox layer. The proposed RFMM is a four-layer feedforward neural network. The generated hyperbox layer and the redefined hyperbox layer are connected through the proposed hyperbox filter, hyperbox optimization and hyperbox combination. The RFMM learning algorithm is an expansion/contraction/redefinition process. The effectiveness of RFMM is evaluated based on ten benchmarks. Experimental results indicate that RFMM leads to better classification performance than various FMM-based, support vector machine-based models and lower sensitivity to the maximum size of expansion coefficient.

Particle swarm optimization (PSO) converges quickly in the initial stage of the search, and is essentially a random search algorithm. Such random search will inevitably lead to a premature convergence problem. In this study, we propose a novel particle swarm optimization enhanced by means of kernel principal component analysis (KPSO). The idea comes from particle swarm optimization imitates human social behavior. By introducing human social behavior, the optimal solution is searched from the overall driving swarm instead of considering only a single optimal particle, preventing particles premature. KPSO is tested on low-dimensional and high-dimensional benchmark functions. Experimental results show that compared with other PSO variants, the KPSO algorithm exhibits competitive performance in terms of accuracy and convergence speed, especially on high-dimensional problems. The KPSO algorithm is also applied to multi-fuel economic dispatch, and the results prove the effectiveness of the proposed method.

This paper considers the time-dependent project scheduling problem (TPSP). We propose a time wave neural network (TWNN) framework that is able to achieve the global optimal solution (viz., the optimal project schedule) of the TPSP, which is very difficult to obtain using conventional methods (e.g., Dijkstra's algorithm). The proposed TWNN is a time wave neuron-based neural network without a requirement for any training. In the design of a TWNN, the overall project network of the TPSP is viewed as a neural network, while each node is considered as a wave-based neuron. With this new perspective, the wave-based neuron is constructed based on seven parts: an input, a wave receiver, a neuron state, a time-window selector, a wave generator, a wave sender, and an output. The first three parts are used to receive the waves coming from the predecessor neurons, the fourth part is used to choose the optimal feasible time window, and the remaining three parts are utilized to generate waves for the successive neurons. The main idea of a TWNN is based on the following mechanism: a wave generated from a neuron (node) means that all previous arcs (subprojects) of this neuron have been completed. In particular, the global optimal project scheduling is obtained when a wave is generated by the final destination neuron. To evaluate the performance of a TWNN, the well-known project scheduling problem library data sets are modified and considered in a comparative analysis. Numerical examples are also utilized to demonstrate the robustness of the method.

This paper presents a hybrid fuzzy wavelet neural network (HFWNN) realized with the aid of polynomial neural networks (PNNs) and fuzzy inference-based wavelet neurons (FIWNs). Two types of FIWNs including fuzzy set inference-based wavelet neurons (FSIWNs) and fuzzy relation inference-based wavelet neurons (FRIWNs) are proposed. In particular, a FIWN without any fuzzy set component (viz., a premise part of fuzzy rule) becomes a wavelet neuron (WN). To alleviate the limitations of the conventional wavelet neural networks or fuzzy wavelet neural networks whose parameters are determined based on a purely random basis, the parameters of wavelet functions standing in FIWNs or WNs are initialized by using the C-Means clustering method. The overall architecture of the HFWNN is similar to the one of the typical PNNs. The main strategies in the design of HFWNN are developed as follows. First, the first layer of the network consists of FIWNs (e.g., FSIWN or FRIWN) that are used to reflect the uncertainty of data, while the second and higher layers consist of WNs, which exhibit a high level of flexibility and realize a linear combination of wavelet functions. Second, the parameters used in the design of the HFWNN are adjusted through genetic optimization. To evaluate the performance of the proposed HFWNN, several publicly available data are considered. Furthermore a thorough comparative analysis is covered.

In this study, we propose a concept of fuzzy wavelet polynomial neural networks (FWPNNs) based on concepts and constructs of polynomial neural networks and fuzzy wavelet neurons (FWNs). These networks exhibit a rule-based architecture while each rule in the FWN consists of the premise part and consequence part. The premise part is realized by using C-means clustering method, while the consequence part is realized by means of wavelet functions whose parameters are estimated with the aid of the least square method. In some sense, the FWPNN can be regarded as a generalized fuzzy wavelet neural network (FWNN). Unlike Gaussian membership functions that are commonly utilized to implement the premise part of the rules in typical FWNNs, C-means method is employed here to overcome a possible curse of dimensionality. Polynomial neural networks (PNNs) are used to express the nonlinearity of a complex system. Furthermore, the particle swarm optimization is used to optimize the design parameters of the proposed network. Based on the PNNs and FWNNs, the proposed FWPNNs take advantages of these two neural networks: it exhibits the abilities to describe high-order nonlinear relations between input and output variables and it is beneficial to describe models impacted by uncertainty. The proposed FWPNNs are applied for time-series prediction and regression problems (e.g., control of dynamic plants). Several well-known modeling benchmarks including regression and time series are considered to evaluate the performance of the proposed FWPNNs. A comparative analysis shows that the proposed FWPNNs result in better performance when comparing with some previous models reported in the literature.

The uncertainty of travel times on a time-dependent network is conventionally considered as randomness or fuzziness. However, sometimes, randomness or fuzziness cannot describe the uncertainty of the travel times on the time-dependent network. In this paper, we introduce a random fuzzy time-dependent network (RFTDN), in which travel times of a time-dependent network are represented as mixed uncertainty of randomness and fuzziness. With these conditions, the resulting RFTDN is far more complex when compared with the known networks. The complexity stems from estimating the length of a path, which is a basic and core issue when analyzing a network. To address this problem, we propose an optimized method that is suitable to cope with the shortest path problem of the RFTDN. The proposed method is realized by means of random fuzzy simulation and a new repair-based genetic optimization. Random fuzzy simulation is used to estimate the random fuzzy functions that describe the length of arcs, whereas the repair-based genetic algorithm is presented for finding the shortest path on the network. Furthermore, the proposed repair-based genetic operators are demonstrated their effectiveness by analyzing running time. A numerical example is also provided to show the robustness of the proposed approach.

In this study, we introduce a Fuzzy Time-Dependent Network (FTDN) and analyze its shortest path problem. The FTDN is a network in which travel times are represented as fuzzy sets and are also time-dependent. Under these circumstances, the shortest path problem on the FTDN is far more complex in comparison with the shortest path problem on the existing networks. To highlight the complexity, we show that on the FTDN, "standard" shortest path algorithms (e.g., the well-known Dijkstra algorithm) are not able to come up with solutions. Subsequently, we construct a suitable method which is suitable to deal with the shortest problem. A fuzzy programming model is presented for finding the shortest path on the FTDN. The proposed model is handled through the techniques which combine mechanisms of fuzzy simulation and genetic optimization. In this particular setting, fuzzy simulation is exploited to estimate the value of uncertain functions, which do not exist in the general networks. The proposed model is evaluated with the use of numerical experimentation. A comparative analysis demonstrates that the proposed model leads to the shortest path while standard algorithms are not capable of finding the path when dealing with the shortest path problem on the FTDN.