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In this study, reinforced fuzzy radial basis function neural networks (FRBFNN) classifier driven by feature extracted data completed with the aid of effectively preprocessing techniques and evolutionary optimization, and its comprehensive design methodology are introduced. An Overall structure of the reinforced FRBFNN comprises the preprocessing part, the premise part and the consequence part of fuzzy rules of the network. In the preprocessing part, four types of preprocessing algorithms such as principal component analysis (PCA), linear discriminant analysis (LDA), combination of PCA and LDA (Hybrid PCA) and fuzzy transform are considered. To extract feature data suitable to characterize signal data, the feature extraction of information data is carried out through the dimensionality reduction done by the preprocessing technique, and then the reduced data are used as the input to the FRBFNN classifier. In the premise part of fuzzy rules of the network, the number of fuzzy rules is determined according to the number of clusters by fuzzy c-means (FCM) clustering. The fitness values of individual fuzzy rules are obtained based on data distribution. In the consequence part of fuzzy rules of the network, the parameters of connection weights located between the hidden layer and the output layer of FRBFNN classifier are estimated by means of the least square estimation. Particle swarm optimization (PSO) is exploited for structural as well as parametric optimization in the FRBFNN classifier. The parameters to be optimized by PSO are related to six factors such as the determination of whether to use data preprocessing, the type of data preprocessing technique, the number of input variables reduced by the preprocessing technique, fuzzification coefficient and the number of fuzzy rules used in fuzzy c-means (FCM) clustering, and the type of connection weights. By using diverse benchmark dataset obtained from UCI repository, the classification performance of the reinforced FRBFNN classifier was evaluated. Through a variety of classification algorithms existed in the Weka data mining software (Weka), the classification performance of the reinforced FRBFNN classifier was compared as well. The superiority of the proposed classifier is demonstrated through Friedman test. Furthermore, we assessed the classification performance of the reinforced FRBFNN classifier applied to black plastic wastes spectral data acquired from Raman and Laser induced breakdown spectroscopy equipment for the practical application of the material sorting system of the black plastic wastes. [ABSTRACT FROM AUTHOR]

Recently, the polynomial-based radial basis function neural networks (P-RBFNNs) have been successfully applied to regression tasks. However, the redundant and non-linear partitioned data easily interfere with accurate partitioning of clusters completed in P-RBFNNs, affecting the regression performance of this existing model. Because the squared error is used as the cost function of the learning method, P-RBFNNs are sensitive to noise interference. In order to cope with these problems, this study introduces a double iterative learning-based polynomial based-RBFNNs (DP-RBFNNs) modeling that focuses on the formation of architectures to improve the accuracy of regression performance as well as enhance the robustness through double iterative learning as follows: a) support vector-based Gaussian kernel fuzzy c-means (SV-GKFCM) as a kind of the support vector-based kernel fuzzy clustering are designed to determine connections (weights) between the input and hidden layers of the proposed model. SV-GKFCM helps effectively reduce the number of redundant data to re-modify the partitioning of clusters in the DP-RBFNNs. In addition, the cluster centers can be accurately updated from the non-linear partitioned data with the aid of Gaussian kernel distance in SV-GKFCM; b) least absolute shrinkage deviations (LASD) as a robust estimation are designed to update connection weights between the hidden and output layers. The SAE (sum of absolute error) function in the LASD method is used as a cost function to reduce the noise interference in the procedure of weight estimation as well as enhance the robustness of the DP-RBFNNs. The superiority of the proposed model is demonstrated through the experimental results. [ABSTRACT FROM AUTHOR]

Fuzzy rule-based models are widely employed to tackle regression problems due to their simplicity and comprehensibility. Numeric functions (e.g., linear ones) are generally utilized to represent the conclusion part of a rule, but this simple module cannot well describe the behavior of data located within local area defined by the premise part. In this study, a novel reinforced fuzzy clustering-based rule model (RFCRM) is presented to address this issue. First, information granulation (Fuzzy C-Means) approach is used to reveal the structure in the data and divide the input space into local regions, as well as form the premise parts. Second, the augmented Random Vector Functional Link Networks (RVFLNs) are employed as the conclusion parts to strengthen the description and representation of the behavior of data positioned within the local regions. Weighted Least Squares Error estimation with regularization is exploited to estimate the coefficients of the connection weights of RVFLN. Also, an exponential weight method benefited from the weight function theory encountered in harmonic analysis is introduced to improve the penalty strategy of regularization in coefficient estimation. More specifically, an exponential weighted ℓ 2 regularization (EW ℓ 2) strategy equipped with the exponential functions as the penalty terms is proposed to realize the targeted penalty on coefficients. The merit of EW ℓ 2 over ordinary ℓ 2 is that different types of polynomial terms can be identified and penalized separately in coefficient estimation. This strategy not only prevents the decline of generalization ability, but also effectively enhances the prediction potential of the model. By combining weighted LSE based on EW ℓ 2 with FCM partition and the augmented RVFLN leads to better prediction accuracy as well as lower complexity (viz., number of rules). Finally, detailed experimental studies are conducted to demonstrate the effectiveness of the proposed RFCRM. [ABSTRACT FROM AUTHOR]

• A novel forecasting model of LSTM-FPNN based on E_RWS is proposed to enhance the generalization abilities for time-series forecasting. • A new neuron driven by deep learning of LSTM is proposed to effectively learn temporal features. • A fuzzy polynomial neuron is used to capture the nonlinear characteristics of the data. • A hybrid selection strategy is developed to effectively increase the diversity of neurons. • The proposed LSTM-FPNN is applied to two practical domain problems to demonstrate its superiority. In this study, we propose a new self-organizing deep network architecture of fuzzy polynomial neural networks (FPNN) based on Fuzzy rule-based Polynomial Neurons (FPNs) and a long short-term memory (LSTM) network to solve the task of time-series forecasting. In the existing regression model based on polynomial neural networks (PNN), it is difficult to achieve high quality performance when predicting time series data, because this model lacks the ability to extract temporal and spatial information. Therefore, we propose a new architecture consisting of one LSTM (temporal) layer and several fuzzy polynomial (spatial) layers to overcome the above-mentioned shortcomings of PNN and enhance its predictive ability to approximate the data. The temporal layer consists of LSTM neurons that have inherently strong modeling capabilities to learn sequential information. The spatial layers are composed of Rule-based Polynomial Neurons (FPNs) that can effectively reflect the complex nonlinear structure found in the input space and granulate it using of the Fuzzy C-Means (FCM) clustering method. An elitism-driven roulette-wheel selection (E_RWS) is used to select appropriate neurons. E_RWS not only ensures that the neuron with the strongest fitting ability is selected but also increases the diversity of candidate neurons. According to the experimental results, the proposed model has a high prediction performance and outperforms many state-of-the-art prediction methods when applied to the real-world time-series. [ABSTRACT FROM AUTHOR]

In this study, a design methodology based on fuzzy relation-based neural networks for stabilized network structure is introduced to cope with over-fitting as well as multi-collinearity problems which generally appear in conventional fuzzy neural networks. The design method of the proposed self-organizing network structure provides an efficient solution to construct the stabilized Fuzzy Relation-based Neural Networks (FRNN) through a synergy of multi-techniques such as ensemble neurons/layers, L2-norm regularization, compromise technique, and multi-optimization, in order to generate the structure of the multi-layered self-organizing network designed with the aid of the learning as well as novel structural design. The overall network structure is realized with the aid of parallel network structure with newly added layers as well as effective node selection method through the combination technique of both a sum of squared coefficients (SSC) and performance index (PI) as a node selection criterion for each layer in FRNN. Ensemble neurons consist of the current inputs and the original inputs, and they serve to reduce the bias of the proposed FRNN by maintaining the information of the original inputs. Also, ensemble layers stand for the combination of the current layer and the front layer, and they play a role for control the variance of the model by taking into account the output of the previous layers. The least square error estimation (LSE)-based learning method with L2-norm regularization is used for constructing the stabilized network architecture, and their ensuring design methodologies result in alleviating the overfitting phenomenon and also enhancing the generalization ability. For the performance enhancement of FRNN directly affected by some parameters such as the number of input variables, collocation of the specific subset of input variables, the number of membership functions per each variable, and the order of polynomial in the consequent parts of the fuzzy rules, multi-particle swarm optimization (MPSO) is exploited for the effectively structural as well as parametric optimization of the proposed networks. That is, the multi-optimization helps achieve a compromise between the better generation performance and the alleviated over-fitting leading to the stabilization of the proposed multi-layered self-organizing network structure realized with the aid of synergistic multi-techniques and ensemble structures such as a) L2-norm regularization-based LSE learning, b) combination technique for effective node selection through the combination of SSC and PI, and c) a novel parallel network structure including newly added layers and node selection method. The performance of the proposed network structure is quantified by comprehensive experiments and comparative analysis. [ABSTRACT FROM AUTHOR]

In recent years, classical fuzzy clustering-based neural networks (FCNNs) have been successfully applied to regression tasks. The determination of the parameters such as cluster centers of the existing hard c-means (HCM) or fuzzy c-means (FCM), leads to the performance deterioration of the model because of the sensitivity of HCM or FCM to noise and outliers. Moreover, there are also several factors for over-fitting and degradation of the robustness of the ensuing model. To solve such problems, two improved clustering techniques and L 2 norm-regularization are considered in the proposed robust fuzzy clustering-based neural networks (RFCNNs) modeling. SVs-based hard c-means (SVs-based HCM) and SVs-based fuzzy c-means (SVs-based FCM) designed with support vectors (SVs) can reduce the interference of uncorrelated data, including noise and outliers, thereby enhancing the main data characteristics effectively, as well as leading to the construction on the improved network model. L 2 norm-regularization can be used to alleviate the degradation of robustness caused by overfitting. In terms of improving the performance of the model through SVs-based HCM or SVs-based FCM, as well as robustness completed through L 2 norm-regularization, the superiority of RFCNNs was verified by experimenting with synthetic data and publicly available data from machine learning datasets. [ABSTRACT FROM AUTHOR]

• We propose fuzzy reinforced polynomial neural networks based on PNN architecture. • We propose fuzzy reinforced polynomial neurons (FRPNs) in the design of FRPNNs. • The proposed FRPNNs is a generalization of hybrid predictors (HPs). In the field of dynamic system identification and prediction, linear models (e.g., autoregressive models), nonlinear models (namely, neural networks models), and hybrid predictors (HPs) that are a hybridization of linear and nonlinear models have been proposed in the past. However, they are not completely free from limitations: they exhibit difficulties to describe high-order nonlinear relations between input and output variables. In this study, we propose fuzzy reinforced polynomial neural networks (FRPNNs), which are polynomial neural network architecture-based on fuzzy reinforced polynomial neurons (FRPNs) to overcome this limitation. The proposed FRPNs that consist of approximation part (AP) and compensation part (CP) arise as novel HPs. Here the CP for modeling nonlinear patterns can be regarded as forming the reinforced part for the AP that aims at capturing linear patterns, while AP is the linear polynomial neuron used in the conventional polynomial neural networks. In some sense, the overall FRPNNs are essentially generalized polynomial neural network architecture with novel HPs. The parameters considered in the design of the proposed fuzzy reinforced polynomial neural networks are optimized with the aid of the particle swarm optimization (PSO). The performance of FRPNNs is discussed involving time series and system identification datasets. Experimental results demonstrate that the proposed FRPNNs achieve at most the accuracy of 43.6% higher in comparison with the accuracy produced by some classical models reported in the literature. [ABSTRACT FROM AUTHOR]

Multiple Support Vector Machine (SVM) classifier based on ensemble learning approaches could be enhanced from the view point of accuracy, but the performance of these classifiers closely depends on the initial condition of the partitioning method used in the design. Furthermore, these classifiers are more easily affected by noise and outliers. In this study, a novel fuzzy quasi-linear SVM classifier realized with the aid of a composite kernel function and Fuzzy C-Means (FCM) clustering is proposed. The objective of this approach is to reduce the effect of noise and outliers and also handle the overfitting problem through the synergistic effect of the two methods: First, Fuzzy C-Means (FCM) is used to partition the training dataset into several subsets as a preprocessing phase of the proposed classifier. Second, the composite kernel based on multiple linear kernel expression is considered to avoid overfitting problem. In more detail, each training data is assigned to the corresponding membership degree. Some data which are potential noise or outliers are assigned with lower membership degrees and thus yield a small contribution to the composite kernel function. Then, the composite kernel function for multiple local SVMs is constructed according to the distribution of training data. The designed fuzzy quasi-linear SVM classifier is tested with both artificial and UCI data sets. It is also applied for sorting the problem of black plastic wastes being handled in the practice in order to verify the effective as well as efficient classification improvement. Experimental results demonstrate that the proposed method shows the elevated classification performance when compared to performance produced by the methods studied previously. [ABSTRACT FROM AUTHOR]

This study focuses on two critical design aspects of a progressive fuzzy polynomial neural network (PFPNN): the influence of the gated recurrent unit (GRU) structure and the implementation of fitness-based candidate neuron selection (FCNS) through two probabilistic strategies. The primary objectives are to enhance modeling accuracy and to reduce the computational load associated with nonlinear regression tasks. Compared with the existing fuzzy rule-based modeling architecture, the proposed dynamic model consists of the GRU structure and the hybrid fuzzy polynomial architecture. In the initial two layers of the PFPNN, we introduce three types of polynomial and fuzzy rules into the GRU neurons (GNs) and fuzzy polynomial neurons (FPNs), which can effectively reveal potential complex relationships in the data space. The synergy of the FCNS strategies and the ℓ 2 regularization learning method is to design a progressive regression model adept at melding the GRU structure with a self-organizing architecture. The proposed GRU structure and polynomial-based neurons significantly improve the modeling accuracy for time-series datasets. The rational utilization of FCNS strategies can reinforce the network structure and discover the potential performance of neurons of the network. Furthermore, the inclusion of ℓ 2 norm regularization provides additional stability to the proposed model and mitigates the overfitting issue commonly encountered in many existing learning methods. We validated the proposed neural networks using six time-series, four machine learning, and two real-world datasets. The PFPNN outperformed other models in the comparison studies in 83.3% of the datasets, emphasizing its superiority in terms of developing a stable deep structure from diverse candidate neurons and reducing computational overhead. [ABSTRACT FROM AUTHOR]

Polynomial neural network (PNN) is a flexible self-organizing network model, and there have been lots of improvements to it. However, various and improved models of PNN do not properly balance their performance and efficiency. In this study, we present novel self-organized hybrid fuzzy neural networks (SHFNN). The purpose of this study is to develop a new design methodology of constructing a hybrid fuzzy model through enhanced input strategy (EIS) and probability-based node selection (PNS) to reinforce the performance of the model without sacrificing efficiency. l 2 -norm regularization (l 2) is utilized to mitigate overfitting as well as enhance generalization capability. The key points of SHFNN can be summarized as follows. First, a hybrid network structure is constructed by combining fuzzy radial basis function neural networks (FRBFNN) and PNN. Second, we propose a probability-based node selection strategy for node (neuron) selection. Third, an enhanced input strategy (EIS) is proposed to design the enhanced input set by merging the general candidate input set (GCIS) and the original candidate input set (OCIS). The regularization coefficient estimation method based on l 2 is used in conjunction with EIS and PNS to improve the performance and enhance the stability of the model. The effectiveness of SHFNN is validated using synthetic and machine learning dataset. The experimental results show that the prediction accuracy of the proposed model is improved by 4–22% when compared with some methods reported in the literature. Statistical analysis is also considered to demonstrate the superiority of the proposed model. [ABSTRACT FROM AUTHOR]

In this study, a face recognition method based on fuzzy transform and radial basis function neural networks is proposed. In order to reduce the dimensionality and extract the important features of face images, fuzzy transform with fuzzy partition techniques is used. Fuzzy radial basis function neural networks (FRBFNNs) are used as a classifier to identify face images into several categories. Radial basis functions are defined by fuzzy C-means clustering method which can analyze the distribution of data points over the input spaces. In order to validate the proposed face recognition system, experimental comparative studies are conducted on the benchmark face datasets such as YALE, ORL, and ABERDEEN databases. A comparative analysis demonstrates that the proposed face recognition system is superior to the conventional face recognition techniques. [ABSTRACT FROM AUTHOR]

This paper is concerned with a new architecture of a reinforced hybrid interval fuzzy neural networks (RHIFNN) classifier developed with aid of Fuzzy C-Means (FCM) clustering and Particle Swarm Optimization (PSO). The key objectives of this study concern the following: (a) selection of preprocessing techniques for the dimensionality reduction of input space. Linear discriminant analysis (LDA) or principal component analysis (PCA) algorithm forms a front end of the network to form the low-dimensional input variables. (b) The efficient process of dealing with uncertain information by interval type-2 fuzzy sets using Fuzzy C-Means (FCM) clustering. The premise (condition) part of the rules is realized by two FCM clustering algorithms, which are invoked by using different values of the fuzzification coefficient subsequently resulting in interval-valued type-2 membership functions. (c) The simultaneous structural and parametric optimization of network by evolutionary algorithm is completed. The parameters of the network including both the premise and consequent parts are optimized by means of the particle swarm optimization (PSO). The proposed classifier is applied to a variety of machine learning datasets and the results are compared with those provided by other classifiers reported in the literature. [ABSTRACT FROM AUTHOR]

In this study, we introduce a novel category of double fuzzy clustering-driven context neural networks (DFCCNNs). The study is focused on the development of advanced design methodologies for redesigning the structure of conventional fuzzy clustering-based neural networks. The conventional fuzzy clustering-based neural networks typically focus on dividing the input space into several local spaces (implied by clusters). In contrast, the proposed DFCCNNs take into account two distinct local spaces called context and cluster spaces, respectively. Cluster space refers to the local space positioned in the input space whereas context space concerns a local space formed in the output space. Through partitioning the output space into several local spaces, each context space is used as the desired (target) local output to construct local models. To complete this, the proposed network includes a new context layer for reasoning about context space in the output space. In this sense, Fuzzy C-Means (FCM) clustering is useful to form local spaces in both input and output spaces. The first one is used in order to form clusters and train weights positioned between the input and hidden layer, whereas the other one is applied to the output space to form context spaces. The key features of the proposed DFCCNNs can be enumerated as follows: (i) the parameters between the input layer and hidden layer are built through FCM clustering. The connections (weights) are specified as constant terms being in fact the centers of the clusters. The membership functions (represented through the partition matrix) produced by the FCM are used as activation functions located at the hidden layer of the “conventional” neural networks. (ii) Following the hidden layer, a context layer is formed to approximate the context space of the output variable and each node in context layer means individual local model. The outputs of the context layer are specified as a combination of both weights formed as linear function and the outputs of the hidden layer. The weights are updated using the least square estimation (LSE)-based method. (iii) At the output layer, the outputs of context layer are decoded to produce the corresponding numeric output. At this time, the weighted average is used and the weights are also adjusted with the use of the LSE scheme. From the viewpoint of performance improvement, the proposed design methodologies are discussed and experimented with the aid of benchmark machine learning datasets. Through the experiments, it is shown that the generalization abilities of the proposed DFCCNNs are better than those of the conventional FCNNs reported in the literature. [ABSTRACT FROM AUTHOR]

In this study, we introduce novel fuzzy neural networks designed with the aid of linear function prototype-driven fuzzy clustering (LFPFC) and layer reconstruction-based network design strategy to deal with the regression problem. The LFPFC constitutes a new clustering technique inspired by the fuzzy c-regression model (FCRM) clustering unlike fuzzy c-means (FCM) clustering LFPFC represents the prototypes of clusters as linear functions, and this can lead to more reliable data analysis of complex regression problems. We propose two types of LFPFC such as an estimated output-based LFPFC and a distance-based LFPFC. The estimated output-based LFPFC uses the output estimated on a basis of the simple model instead of the target output to calculate the centroid of LFPFC. A centroid of distance-based LFPFC is computed through the Euclidean distance between input data and the centroid of the cluster. By using two kinds of LFPFC approaches, we propose three different types of fuzzy neural networks: i) the fuzzy neural networks through layer reconstruction-based network design strategy consists of two models. The first model serves as an estimate of the desired output and the estimated output is used in the LFPFC of the second model. ii) In the fuzzy neural networks applied to the basic architecture of distance-based LFPFC, the hidden layer using the membership function changes to basic distance-based LFPFC, and the partition matrix obtained from LFPFC is used as the output of the hidden layer. iii) in the fuzzy neural network with the advanced architecture of distance-based LFPFC, an additional auxiliary layer is considered between the hidden and output layers to estimate the membership function of output space through LFPFC. In the experiments, we evaluate the performance index of the proposed models using publicly available machine learning datasets. The superiority of the proposed fuzzy neural networks designed by using LFPFC is demonstrated through the comparative analysis with the diverse regression models offered in the Weka data mining software. By conducting the Friedman test we show that the proposed model exhibits visible competitiveness from the viewpoint of performance. In addition, a real-world Portland cement dataset is dealt with to demonstrate the superiority of the models designed with the aid of LFPFC and reinforced layer reconstruction-based network design strategy. [ABSTRACT FROM AUTHOR]

Convolutional neural networks (CNNs) have attracted increasing attention in recent years because of their powerful abilities to extract and represent spatial/temporal information. However, for general data, its features are assumed to have weak or no correlation, and directly applying CNN to classify such data could result in poor classification performance. To address this problem, a combined technique of original data representation method of fuzzy penalty function-based constrained particle swarm optimization (FCPSO) and CNN, so-called FCPSO-CNN is designed to effectively solve the classification problems for generic dataset and applied to recognize (classify) black plastic wastes in recycling problems. In more detail, CPSO is introduced to optimize feature reordering matrix under constraints and the construction of this matrix is driven by fitness function of CNN that quantifies classification performance. The Mamdani type fuzzy inference system (FIS) is employed to realize the fuzzy penalty function (FPF) which is utilized to realize the constrained problems of CPSO as well as alleviate the issues of the original penalty function method suffering from the lack of robustness. Experimental results demonstrate that FCPSO-CNN achieves the best classification accuracy on 13 out of 17 datasets; the statistical analysis also confirms the superiority of FCPSO-CNN. An interesting point is worth to mention that some feature reordering matrices in the infeasible space come with better classification accuracy. It has been found that the proposed method results in more accurate solution than one-dimensional CNN, random reordering feature-based CNN and some well-known classifiers (e.g., Naive Bayes, Multilayer perceptron, Support vector machine). • CNN design based on the novel data representation method leads to preferred classifier. • CPSO is applied to acquire the available features reordering matrix with spatial information from many matrices. • FPF is employed to copy with CO problem, which combines the FIS to self-adaptively modify penalty parameter. • Visualization technique of t-SNE is applied to the proposed data representation method. • The proposed FCPSO is applied to solve the real-life problem of black plastic wastes. [ABSTRACT FROM AUTHOR]

This paper is concerned with a reinforced rule-based fuzzy model and its design realized with the aid of fuzzy clustering. The objective of this study is to develop a new design methodology of constructing incremental fuzzy rules formed through fuzzy clustering. The proposed model consists of four functional modules. The premise part of the fuzzy rules involves membership functions designed with the aid of the Fuzzy C-Means (FCM) clustering algorithm. The consequent part comprises local models (linear functions). The parameters of the local models are estimated by Weighted Least Squares (WLS). In the inference part, after determining the error associated with each fuzzy rule, the rule with the highest error is identified and refined. The selected rule is split into two or more specialized more detailed rules providing a better insight and detailed view into the system. These new rules are formed with the aid of the context-based Fuzzy C-Means (C-FCM) clustering. Along with the refinement of the rule, the linear conclusion part can be also refined by admitting quadratic functions. The effectiveness of the proposed rule-based model is discussed and illustrated with the aid of some numeric studies including both synthetic and machine learning data. [ABSTRACT FROM AUTHOR]

This study is concerned with a design of a face recognition algorithm realized based on feature extraction with the aid of the 2-directional 2-dimensional linear discriminant analysis referred to as (2D) 2 LDA. The 2DLDA algorithm yields high accuracy, but comes with an unresolved problem of handling large feature matrices present in face recognition problems. The proposed (2D) 2 LDA algorithm is computationally more efficient and produces more powerful discrimination decision. The proposed P-RBF NNs is used as a recognition module. The architecture of this module consists of three functional components. The coefficients of the P-RBF NNs model are obtained by fuzzy inference method forming the inference part of fuzzy rules. The essential design parameters (including learning rate, momentum, fuzzification coefficient, and the feature selection mechanism) of the networks are optimized by means of differential evolution (DE). The experimental results reported for benchmark face datasets – the Yale, ORL database, and IC&CI dataset demonstrate the effectiveness and efficiency of (2D) 2 LDA algorithm compared with other pre-processing approaches such as LPP, 2D-PCA, 2D-LPP, SR, PCA, (2D) 2 PCA and fusion of PCA-LDA. The experimental results show that (2D) 2 LDA based P-RBF NNs achieves higher performance than being reported by other methods. [ABSTRACT FROM AUTHOR]

• Overall structural framework designed for the restoration of motion-blurred images is proposed with the aid of PSO-based parameter estimation and image quality assessment. • The proposed Image Restoration Framework has a complete function which can effectively enhance the restored image quality. • Blur parameter estimation algorithm based on PSO (BPPO) is employed to optimize the motion-blurred parameter estimation. • A polynomial-based radial basis function neural network is used as image quality evaluation method to evaluate restored image quality for efficient classification. The restoration of motion-blurred images has always been a complex problem in image restoration. The current single blurred image algorithm cannot very well solve the estimation error of motion blur parameters. A comprehensive motion-blurred image restoration framework is proposed, which includes motion-blurred data generation, blur parameter estimation, and image quality assessment of restored images. First, we designed and used four image data sets with different degrees of blurring. We innovatively propose a blur parameter estimation algorithm based on the particle swarm optimization (B-PSO) algorithm. The Naturalness Image Quality Evaluator (NIQE) is used as the fitness function of the PSO algorithm. The framework also introduces a polynomial-based radial basis function neural network (P-RBFNN) as a new image quality assessment (IQA) method , with good image classification performance. Test results from public datasets show that the proposed framework can accurately estimate blur parameters. The peak signal-to-noise ratio (PSNR) reaches 29.976 dB, the structural similarity (SSIM) reaches 0.9044, and the classification rate is 96%. The proposed restoration framework produces the best image restoration results. [ABSTRACT FROM AUTHOR]

• The convolution-base and composite kernel are used for alleviating overfitting. • The composite kernel could adjust the nonlinear fitting ability of the classifier. • Hybrid fuzzy multi-(HFM) SVM leads to better results with flexible feature fusion. • The effectiveness of the HFM-SVM is demonstrated by three practical applications. Lately, Convolutional Neural Networks (CNNs) have been introduced to extract features and further enhance the classification performance in different application areas. In this study, a hybrid fuzzy multiple (HFM)-SVM design with the convolution-base (which consists of a series of pooling and convolutional layers) and composite kernel function is proposed. The objective of the proposed classifier is to enhance the nonlinear fitting ability of the classifier and improve the classification performance in high-dimensional applications. The key points of the proposed HFM SVM are enumerated as follows: 1) The convolution-base of the proposed classifier extracts features. The extracted features exhibit flexibility and applicability in high-dimensional applications. 2) The proposed HFM SVM designed with the composite kernel could adjust the nonlinear fitting ability for improving classification performance. The procedure of the proposed HFM SVM is described as follows: Convolution-base is considered as a preprocessing unit for extracting features. The features are not always linearly separable especially when being extracted from high dimensional data. A composite kernel function is constructed by considering the complicated (nonlinear) classification boundary into several local linear boundaries. The structure of the extracted features is captured by FCM clustering and integrated into the composite kernel function for enhancing the nonlinear fitting ability of the proposed classifier. The nonlinearity of the composite function can fill the gap between linear and nonlinear kernel functions by adjusting the number of clusters obtained by the FCM clustering algorithm. The proposed HFM SVM classifier based on composite kernel could improve the classification performance on high dimensional datasets. The performance of the proposed HFM SVM is experimented with and demonstrated by using three high-dimensional applications to show the effectiveness as well as performance improvement. [ABSTRACT FROM AUTHOR]

• AFS and RS are used to effectively obtain the transmittance spectra of black plastic wastes not available in the existing NIR. • A feature selection method of the peak points is considered based on the analysis of chemical information for low cost spectrometer by using a small amount of input variables. • A method of 2D reconstruction through mapping from 1D signal data based on peak points is proposed to effectively deal with spatial structure information between data. • 2DCNN design driven by 2D information features or chemical peak points data leads to high performance as well as anti-noise capability through effective data mapping. In this study, two types of convolutional neural network (CNN) classifiers are designed to handle the problem of classifying black plastic wastes. In particular, the black plastic wastes have the property of absorbing laser light coming from spectrometer. Therefore, the classification of black plastic wastes remains still a challenging problem compared to classifying other colored plastic wastes using existing spectroscopy (i.e., NIR). When it comes the classification problem of black plastic wastes, effective classification techniques by the laser spectroscopy of Fourier Transform-Infrared Radiation (FT-IR) with Attenuated Total Reflectance (ATR) and Raman to analyze the classification problem of black plastic wastes are introduced. Due to the strong ability of extracting spatial features and remarkable performance in image classification, 1D and 2D CNN through data features are designed as classifiers. The technique of chemical peak points selection is considered to reduce data redundancy. Furthermore, through the selection of data features based on the extracted 1D data with peak points is introduced. Experimental results demonstrate that 2DCNN classifier designed with the help of 2D data feature selection as well as 1DCNN classifier shows the best performance compared with other reported methods for classifying black plastic wastes. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new architecture of optimized Radial Basis Function neural network classifier developed with the aid of fuzzy clustering and data preprocessing techniques and discuss its comprehensive design methodology. In the preprocessing part, the Linear Discriminant Analysis (LDA) or Principal Component Analysis (PCA) algorithm forms a front end of the network. The transformed data produced here are used as the inputs of the network. In the premise part, the Fuzzy C-Means (FCM) algorithm determines the receptive field associated with the condition part of the rules. The connection weights of the classifier are of functional nature and come as polynomial functions forming the consequent part. The Particle Swarm Optimization algorithm optimizes a number of essential parameters needed to improve the accuracy of the classifier. Those optimized parameters include the type of data preprocessing, the dimensionality of the feature vectors produced by the LDA (or PCA), the number of clusters (rules), the fuzzification coefficient used in the FCM algorithm and the orders of the polynomials of networks. The performance of the proposed classifier is reported for several benchmarking data-sets and is compared with the performance of other classifiers reported in the previous studies. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a new passive auto focusing algorithm to acquire images with enhanced quality through a digital camera. The focus measure operations play a key role in a passive auto focusing method. The proposed focus measure operation is based on a localized version of image variance method. The localization of the image variance focus measure operation can be implemented with the use of fuzzy partition and Fuzzy Transform. In order to validate our approach, experimental comparative studies are conducted on test images with the use of different focus measure operators. The selected operators have been chosen from an extensive review of the state-of-the-art approaches. A comparative analysis demonstrates that the proposed algorithm is superior to the conventional methods. [ABSTRACT FROM AUTHOR]

In this study, we propose a hybrid method of face recognition by using face region information extracted from the detected face region. In the preprocessing part, we develop a hybrid approach based on the Active Shape Model (ASM) and the Principal Component Analysis (PCA) algorithm. At this step, we use a CCD (Charge Coupled Device) camera to acquire a facial image by using AdaBoost and then Histogram Equalization (HE) is employed to improve the quality of the image. ASM extracts the face contour and image shape to produce a personal profile. Then we use a PCA method to reduce dimensionality of face images. In the recognition part, we consider the improved Radial Basis Function Neural Networks (RBF NNs) to identify a unique pattern associated with each person. The proposed RBF NN architecture consists of three functional modules realizing the condition phase, the conclusion phase, and the inference phase completed with the help of fuzzy rules coming in the standard ‘if-then’ format. In the formation of the condition part of the fuzzy rules, the input space is partitioned with the use of Fuzzy C-Means (FCM) clustering. In the conclusion part of the fuzzy rules, the connections (weights) of the RBF NNs are represented by four kinds of polynomials such as constant, linear, quadratic, and reduced quadratic. The values of the coefficients are determined by running a gradient descent method. The output of the RBF NNs model is obtained by running a fuzzy inference method. The essential design parameters of the network (including learning rate, momentum coefficient and fuzzification coefficient used by the FCM) are optimized by means of Differential Evolution (DE). The proposed P-RBF NNs (Polynomial based RBF NNs) are applied to facial recognition and its performance is quantified from the viewpoint of the output performance and recognition rate. [ABSTRACT FROM AUTHOR]

In this study, we propose Hybrid Radial Basis Function Neural Networks (HRBFNNs) realized with the aid of fuzzy clustering method (Fuzzy C-Means, FCM) and polynomial neural networks. Fuzzy clustering used to form information granulation is employed to overcome a possible curse of dimensionality, while the polynomial neural network is utilized to build local models. Furthermore, genetic algorithm (GA) is exploited here to optimize the essential design parameters of the model (including fuzzification coefficient, the number of input polynomial fuzzy neurons (PFNs), and a collection of the specific subset of input PFNs) of the network. To reduce dimensionality of the input space, principal component analysis (PCA) is considered as a sound preprocessing vehicle. The performance of the HRBFNNs is quantified through a series of experiments, in which we use several modeling benchmarks of different levels of complexity (different number of input variables and the number of available data). A comparative analysis reveals that the proposed HRBFNNs exhibit higher accuracy in comparison to the accuracy produced by some models reported previously in the literature. [ABSTRACT FROM AUTHOR]

Abstract: Fuzzy modeling of complex systems is a challenging task, which involves important problems of dimensionality reduction and calls for various ways of improving the accuracy of modeling. The IG-FRBFNN, a hybrid architecture of the IG-FIS (Fuzzy Inference System) and FRBFNN (Fuzzy Radial Basis Function Neural Networks), is proposed to address these problems. The paper is concerned with the analysis and design of IG-FRBFNNs and their optimization by means of the Hierarchical Fair Competition-based Parallel Genetic Algorithm (HFC-PGA). In the proposed network, the membership functions of the premise part of the fuzzy rules of the IG-based FRBFNN model directly rely on the computation of the relevant distance between data points and the use of four types of polynomials such as constant, linear, quadratic and modified quadratic are considered for the consequent part of fuzzy rules. Moreover, the weighted Least Square (WLS) learning is exploited to estimate the coefficients of the polynomial forming the conclusion part of the rules. Since the performance of the IG-RBFNN model is affected by some key design parameters, such as a specific subset of input variables, the fuzzification coefficient of the FCM, the number of rules, and the order of polynomial of the consequent part of fuzzy rules, it becomes beneficial to carry out both structural as well as parametric optimization of the network. In this study, the HFC-PGA is used as a comprehensive optimization vehicle. The performance of the proposed model is illustrated by means of several representative numerical examples. [Copyright &y& Elsevier]

Abstract: In this study, we introduce a new design methodology of granular-oriented self-organizing Hybrid Fuzzy polynomial neural networks (HFPNN) that is based on multi-layer perceptron with context-based polynomial neurons (CPNs) or polynomial neurons (PNs). In contrast to the typical architectures encountered in polynomial neural networks (PNN), our main objective is to develop a design strategy of HFPNN as follows: (a) The first layer of the proposed network consists of context-based polynomial neuron (CPN). Here CPN is fully reflective of the structure encountered in numeric data which are granulated with the aid of context-based fuzzy c-means (C-FCM) clustering method. The context-based clustering supporting the design of information granules is completed in the space of the input data (input variables) while the formation of the clusters here is guided by a collection of some predefined fuzzy sets (so-called contexts) specified in the output space. (b) The proposed design procedure being applied to each layer of HFPNN leads to the selection of the preferred nodes of the network (CPNs or PNs) whose local characteristics (such as the number of contexts, the number of clusters, a collection of the specific subset of input variables, and the order of the polynomial) can be easily adjusted. These options contribute to the flexibility as well as simplicity and compactness of the resulting architecture of the network. For the evaluation of the performance of the proposed HFPNN, we use well-known machine learning data coming from the machine learning repository. [Copyright &y& Elsevier]

Abstract: In this study, polynomial-based radial basis function neural networks are proposed as one of the functional components of the overall face recognition system. The system consists of the preprocessing and recognition module. The design methodology and resulting procedure of the proposed P-RBF NNs are presented. The structure helps construct a solution to high-dimensional pattern recognition problems. In data preprocessing part, principal component analysis (PCA) is generally used in face recognition. It is useful in reducing the dimensionality of the feature space. However, because it is concerned with the overall face image, it cannot guarantee the same classification rate when changing viewpoints. To compensate for these limitations, linear discriminant analysis (LDA) is used to enhance the separation between different classes. In this paper, we elaborate on the PCA-LDA algorithm and design an optimal P-RBF NNs for the recognition module. The proposed P-RBF NNs architecture consists of three functional modules such as the condition part, the conclusion part, and the inference part realized in terms of fuzzy “if–then” rules. In the condition part of fuzzy rules, the input space is partitioned with the use of fuzzy clustering realized by means of the Fuzzy C-Means (FCM) algorithm. In the conclusion part of rules, the connection weight is realized through three types of polynomials such as constant, linear, and quadratic. The coefficients of the P-RBF NNs model are obtained by fuzzy inference method forming the inference part of fuzzy rules. The essential design parameters (including learning rate, momentum, fuzzification coefficient, and the feature selection mechanism) of the networks are optimized by means of differential evolution (DE). The experimental results completed on benchmark face datasets – the AT&T, and Yale datasets demonstrate the effectiveness and efficiency of PCA-LDA combined algorithm compared with other algorithms such as PCA, LPP, 2D-PCA and 2D-LPP. A real time face recognition system realized in this way is also presented. [Copyright &y& Elsevier]

Abstract: In this study, we discuss a design of an optimized cascade fuzzy controller for the rotary inverted pendulum system and ball & beam system by using an optimization vehicle of differential evolution (DE). The structure of the differential evolution optimization environment is simple and a convergence to optimal values realized here is very good in comparison to the convergence reported for other optimization algorithms. DE is easy to use given its mathematical operators. It also requires a limited computing overhead. The rotary inverted pendulum system and ball & beam system are nonlinear systems, which exhibit unstable motion. The performance of the proposed fuzzy controller is evaluated from the viewpoint of several performance criteria such as overshoot, steady-state error, and settling time. Their values are obtained through simulation studies and practical, real-world experiments. We evaluate and analyze the performance of the proposed optimal fuzzy controller optimized by Genetic Algorithm (GA), and DE. In this setting, we show the superiority of DE versus other methods being used here as well as highlight the characteristics of this optimization tool. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce an advanced architecture of K-means clustering-based polynomial Radial Basis Function Neural Networks (p-RBF NNs) designed with the aid of Particle Swarm Optimization (PSO) and Differential Evolution (DE) and develop a comprehensive design methodology supporting their construction. The architecture of the p-RBF NNs comes as a result of a synergistic usage of the evolutionary optimization-driven hybrid tools. The connections (weights) of the proposed p-RBF NNs being of a certain functional character and are realized by considering four types of polynomials. In order to design the optimized p-RBF NNs, a prototype (center value) of each receptive field is determined by running the K-means clustering algorithm and then a prototype and a spread of the corresponding receptive field are further optimized through running Particle Swarm Optimization (PSO) and Differential Evolution (DE). The Weighted Least Square Estimation (WLSE) is used to estimate the coefficients of the polynomials (which serve as functional connections of the network). The performance of the proposed model and the comparative analysis involving models designed with the aid of PSO and DE are presented in case of a nonlinear function and two Machine Learning (ML) datasets [Copyright &y& Elsevier]

Abstract: In this study, we introduce a new design methodology of fuzzy radial basis function-based polynomial neural networks. In many cases, these models do not come with capabilities to deal with granular information. With this regard, fuzzy sets offer several interesting and useful opportunities. This study presents the development of fuzzy radial basis function-based neural networks augmented with virtual input variables. The performance of the proposed category of models is quantified through a series of experiments, in which we use two machine learning data sets and two publicly available software development effort data. [Copyright &y& Elsevier]

Abstract: In this study, we introduce the design methodology of an optimized fuzzy controller with the aid of particle swarm optimization (PSO) for ball and beam system. The ball and beam system is a well-known control engineering experimental setup which consists of servo motor, beam and ball. This system exhibits a number of interesting and challenging properties when being considered from the control perspective. The ball and beam system determines the position of ball through the control of a servo motor. The displacement change of the position of ball leads to the change of the angle of the beam which determines the position angle of a servo motor. The fixed membership function design of type-1 based fuzzy logic controller (FLC) leads to the difficulty of rule-based control design when representing linguistic nature of knowledge. In type-2 FLC as the expanded type of type-1 FL, we can effectively improve the control characteristic by using the footprint of uncertainty (FOU) of the membership functions. Type-2 FLC exhibits some robustness when compared with type-1 FLC. Through computer simulation as well as real-world experiment, we apply optimized type-2 fuzzy cascade controllers based on PSO to ball and beam system. To evaluate performance of each controller, we consider controller characteristic parameters such as maximum overshoot, delay time, rise time, settling time, and a steady-state error. In the sequel, the optimized fuzzy cascade controller is realized and also experimented with through running two detailed comparative studies including type-1/type-2 fuzzy controller and genetic algorithms/particle swarm optimization. [Copyright &y& Elsevier]

Abstract: In this study, we design polynomial-based radial basis function neural networks (P-RBF NNs) based on a fuzzy inference mechanism. The essential design parameters (including learning rate, momentum coefficient and fuzzification coefficient of the underlying clustering method) are optimized by means of the particle swarm optimization. The proposed P-RBF NNs dwell upon structural findings about training data that are expressed in terms of a partition matrix resulting from fuzzy clustering in this case being the fuzzy C-means (FCM). The network is of functional nature as the weights between the hidden layer and the output are some polynomials. The use of the polynomial weights becomes essential in capturing the nonlinear nature of data encountered in regression or classification problems. From the perspective of linguistic interpretation, the proposed network can be expressed as a collection of “if–then” fuzzy rules. The architecture of the networks discussed here embraces three functional modules reflecting the three phases of input–output mapping realized in rule-based architectures, namely condition formation, conclusion creation, and aggregation. The proposed classifier is applied to some synthetic and machine learning datasets, and its results are compared with those reported in the previous studies. [Copyright &y& Elsevier]

Abstract: In this study, we develop a design methodology for a fuzzy PD cascade controller for a ball & beam system by using particle swarm optimization (PSO). The ball & beam system is a well-known control engineering experimental setup, which consists of servo motor, beam, and ball. This system exhibits a number of interesting and challenging properties when being considered from the control perspective. The ball & beam system determines the position of ball through the control of a servo motor. The displacement change of the position of ball leads to the change of the angle of the beam which determines the position angle of a servo motor. Consequently the variation of the position of the moving ball and the ensuing change of the angle of the beam results in the change of the position angle of a servo motor. We introduce a fuzzy PD cascade controller scheme which consists of the outer (1st) controller and the inner (2nd) controller arranged in a cascaded architecture. Auto-tuning of the parameters of the controller (scaling factors) as well as fuzzy rules of each fuzzy PD controller is realized with the use of the PSO. Moreover the comparative analysis of results of optimization realized by PSO and GA based on SGA (Serial Genetic Algorithms) is discussed from the viewpoint of control performance. The set-point value of the inner controller (the 2nd controller) corresponds to the position angle of a servo motor, and is given as reference value, which enters into the inner controller as the 2nd controller of the two cascaded controllers. The optimization process takes advantage of a rapid convergence of PSO being used here as a generic search mechanism. A detailed comparative analysis carried out from the viewpoint of the performance and the design methodology, is provided for the fuzzy PD cascade controller and the conventional PD cascade controller whose design exploited serial genetic algorithms. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce a new category of fuzzy models called a fuzzy ensemble of parallel polynomial neural network (FEP2N2), which consist of a series of polynomial neural networks weighted by activation levels of information granules formed with the use of fuzzy clustering. The two underlying design mechanisms of the proposed networks rely on information granules resulting from the use of fuzzy C-means clustering (FCM) and take advantage of polynomial neural networks (PNNs). The resulting model comes in the form of parallel polynomial neural networks. In the design procedure, in order to estimate the optimal values of the coefficients of polynomial neural networks we use a weighted least square estimation algorithm. We incorporate various types of structures as the consequent part of the fuzzy model when using the learning algorithm. Among the diverse structures being available, we consider polynomial neural networks, which exhibit highly nonlinear characteristics when being viewed as local learning models. We use FCM to form information granules and to overcome the high dimensionality problem. We adopt PNNs to find the optimal local models, which can describe the relationship between the input variables and output variable within some local region of the input space. We show that the generalization capabilities as well as the approximation abilities of the proposed model are improved as a result of using polynomial neural networks. The performance of the network is quantified through experimentation in which we use a number of benchmarks already exploited within the realm of fuzzy or neurofuzzy modeling. [Copyright &y& Elsevier]

Abstract: In this study, we present a design of an optimized fuzzy cascade controller based on Hierarchical Fair Competition-based Genetic Algorithms (HFCGA) for a rotary inverted pendulum system. In this system, one controls the movement of a pendulum through the adjustment of a rotating arm. The objective is to control the position of the rotating arm and to make the pendulum maintain the unstable equilibrium point at vertical position. To control the system, we design a fuzzy cascade controller scheme which consists of two fuzzy controllers arrange in a cascaded topology. The parameters of the controller are optimized by means of the HFCGA algorithm. The fuzzy cascade scheme comprises two controllers located in two loops. An inner loop controller governs the position of the rotating arm while an outer controller modifies a set point of the inner controller implied by the changes of the angle of pendulum. The HFCGA being a computationally effective scheme of the Parallel Genetic Algorithm (PGA) has been developed to eliminate an effect of premature convergence encountered in Serial Genetic Algorithms (SGA). It has emerged as an effective optimization vehicle to deal with very large search spaces. A comparative analysis involving computing simulations and practical experiment demonstrates that the proposed HFCGA based fuzzy cascade controller comes with superb performance in comparison with the conventional Linear Quadratic Regulator (LQR) controller as well as HFCGA-based PD cascade controller. [Copyright &y& Elsevier]

Abstract: The paper is concerned with a hybrid optimization of fuzzy inference systems based on hierarchical fair competition-based parallel genetic algorithms (HFCGA) and information granulation. The process of information granulation is realized with the aid of the C-Means clustering. HFCGA being a multi-population based parallel genetic algorithms (PGA) is exploited here to realize structure optimization and carry out parameter estimation of the fuzzy models. The HFCGA becomes helpful in the context of fuzzy models as it restricts a premature convergence encountered quite often in optimization problems. It concerns a set of parameters of the model including among others the number of input variables to be used, a specific subset of input variables, and the number of membership functions. In the hybrid optimization process, two general optimization mechanisms are explored. The structural development of the fuzzy model is realized via the HFCGA optimization and C-Means, whereas to deal with the parametric optimization we proceed with a standard least square method and the use of the HFCGA technique. A suite of comparative studies demonstrates that the proposed algorithm leads to the models whose performance is superior in comparison with some other constructs commonly used in fuzzy modeling. [Copyright &y& Elsevier]

Abstract: In this study, we introduce a design methodology for an optimized fuzzy cascade controller for ball and beam system by exploiting the use of hierarchical fair competition-based genetic algorithm (HFCGA). The ball and beam system is a well-known control engineering experimental setup which consists of servo motor, beam and ball and exhibits a number of interesting and challenging properties when considered from the control perspective. The position of ball is determined through the control of a servo motor. The displacement change of the position of ball requires the change of the angle of the beam which determines the position angle of a servo motor. Consequently, the variation of the position of the moving ball and the ensuing change of the angle of the beam results in the change of the position angle of a servo motor. We introduce the fuzzy cascade controller scheme which consists of the outer (1st) controller and the inner (2nd) controller in a cascaded architecture. Auto-tuning of the parameters of the controller (viz. scaling factors) of each fuzzy controller is realized with the use of the HFCGA. The set-point value of the inner controller (the 2nd controller) corresponds to the position angle of a servo motor, and is given as a reference value which enters into the inner controller as the 2nd controller of the two cascaded controllers. HFCGA is a kind of a parallel genetic algorithm (PGA), which helps alleviate an effect of premature convergence being a potential shortcoming present in conventional genetic algorithms (GAs). A detailed comparative analysis carried out from the viewpoint of the performance and the design methodology, is provided for the fuzzy cascade controller and the conventional PD cascade controller whose design relied on the use of the serial genetic algorithms. [Copyright &y& Elsevier]

Abstract: The paper is concerned with the identification of fuzzy inference systems (fuzzy models) realized with the aid of the successive tuning method using a variant identification ratio that is based on Hierarchical Fair Competition-based Parallel Genetic Algorithms (HFC-PGA) and information granulation. The HFC-PGA is a certain multi-population version of Parallel Genetic Algorithms (PGA), which is suitable for a simultaneous optimization of both the structure of the fuzzy model as well as its parameters. The granulation of information is realized with the aid of the C-Means clustering algorithm. Information granules formed in this way become essential at further stages of the construction of the fuzzy models by forming the centers (modal values) of the fuzzy sets constituting individual rules of the inference schemes. Further optimization of the fuzzy model deals with an adjustment of a suite of parameters (such as the number of input variables to be used in the model, a collection of specific subsets of the input variables, and the number of membership functions) being used by these variables, and the order and parameters of the polynomial occurring in the conclusions of the corresponding rules. An iterative development of the fuzzy model deals with its structural as well as parametric optimization via HFC-PGA, the C-Means algorithm, and a standard least square estimation method. To evaluate the performance of the proposed model, we exploit well known and commonly used data sets such as gas furnace, Mackey–Glass time series as well as medical imaging system. A comparative analysis demonstrates that the proposed model leads to the superior performance when compared with other fuzzy models reported in the literature. [Copyright &y& Elsevier]

Abstract: We introduce a design procedure for fuzzy systems using the concept of information granulation and genetic optimization. Information granulation and resulting information granules themselves become an important design aspect of fuzzy models. By accommodating the formalism of fuzzy sets, the model is geared towards capturing relationship between information granules (fuzzy sets) rather than concentrating on plain numeric data. Information granulation realized with the use of the standard C-Means clustering helps determine the initial values of the parameters of the fuzzy models. This in particular concerns such essential components of the rules as the initial apexes of the membership functions standing in the premise part of the fuzzy rules and the initial values of the polynomial functions standing in the consequence part. The initial parameters are afterwards tuned with the aid of the genetic algorithms (GAs) and the least square method (LSM). The overall design methodology arises as a hybrid development process involving structural and parametric optimization. Especially, genetic algorithms and C-Means are used to generate the structurally as well as parametrically optimized fuzzy model. To identify the structure and estimate parameters of the fuzzy model we exploit the methodologies such as joint and successive method realized by means of genetic algorithms. The proposed model is evaluated using experimental data and its performance is contrasted with the behavior of the fuzzy models available in the literature. [Copyright &y& Elsevier]

Abstract: In this study, we introduce and investigate a new topology of fuzzy-neural networks—fuzzy polynomial neural networks (FPNN) that is based on a genetically optimized multiplayer perceptron with fuzzy set-based polynomial neurons (FSPNs). We also develop a comprehensive design methodology involving mechanisms of genetic optimization and information granulation. In the sequel, the genetically optimized FPNN (gFPNN) is formed with the use of fuzzy set-based polynomial neurons (FSPNs) composed of fuzzy set-based rules through the process of information granulation. This granulation is realized with the aid of the C-means clustering (C-Means). The design procedure applied in the construction of each layer of an FPNN deals with its structural optimization involving the selection of the most suitable nodes (or FSPNs) with specific local characteristics (such as the number of input variable, the order of the polynomial, the number of membership functions, and a collection of specific subset of input variables) and address main aspects of parametric optimization. Along this line, two general optimization mechanisms are explored. The structural optimization is realized via genetic algorithms (GAs) and HCM method whereas in case of the parametric optimization we proceed with a standard least square estimation (learning). Through the consecutive process of structural and parametric optimization, a flexible neural network is generated in a dynamic fashion. The performance of the designed networks is quantified through experimentation where we use two modeling benchmarks already commonly utilized within the area of fuzzy or neurofuzzy modeling. [Copyright &y& Elsevier]

Abstract: In this study, we introduce a new architecture of hybrid fuzzy neural networks (gHFNNs) and offer a comprehensive design methodology that supports their development. The gHFNN rule-based architecture results from a synergistic usage of Fuzzy Neural Networks (FNNs) with Polynomial Neural Networks (PNNs). The FNN contributes to the formation of the premise part of the overall network of the gHFNN. The consequence part of the gHFNN is designed taking advantage of PNNs. The optimization of the FNN is realized with the aid of a standard back-propagation learning combined with genetic optimization. The development of the PNN dwells on the extended Group Method of Data Handling (GMDH) and Genetic Algorithms (GAs). Through the consecutive process of such structural and parametric optimization, an optimized topology of the PNN becomes generated in a dynamic fashion. The performance of the gHFNN is evaluated through a series of numeric experiments. A comparative analysis shows that the proposed gHFNN is characterized by higher accuracy as well as significant predictive capabilities when contrasted with other neurofuzzy models presented in the literature. [Copyright &y& Elsevier]

Abstract: In this study, we introduce a new topology of Fuzzy Polynomial Neural Networks (FPNN) that is based on a genetically optimized multilayer perceptron with fuzzy polynomial neurons (FPNs) and discuss its comprehensive design methodology. The underlying methodology involves mechanisms of genetic optimization, especially genetic algorithms (GAs). Let us recall that the design of the “conventional” FPNNs uses an extended Group Method of Data Handling (GMDH) and exploits a fixed fuzzy inference type located at each FPN of the FPNN as well as considers a fixed number of input nodes at FPNs (or nodes) located in each layer. The proposed FPNN gives rise to a structurally optimized structure and comes with a substantial level of flexibility in comparison to the one we encounter in conventional FPNNs. The structural optimization is realized via GAs whereas in the case of the parametric optimization we proceed with a standard least square method based learning. Through the consecutive process of such structural and parametric optimization, an optimized and flexible fuzzy neural network is generated in a dynamic fashion. The performance of the proposed gFPNN is quantified through experimentation that exploits standard data already being used in fuzzy modeling. The results reveal superiority of the proposed networks over the existing fuzzy and neural models. [Copyright &y& Elsevier]

Abstract: We introduce a new architecture of hybrid fuzzy polynomial neural networks (HFPNN) that is based on a genetically optimized multi-layer perceptron and develop their comprehensive design methodology involving mechanisms of genetic optimization. The construction of HFPNN exploits fundamental technologies of computational intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms (GAs). The architecture of the resulting genetically optimized HFPNN (namely gHFPNN) results from a synergistic usage of the hybrid system generated by combining fuzzy polynomial neurons (FPNs)-based fuzzy neural networks (FNN) with polynomial neurons (PNs)-based polynomial neural networks (PNN). The design of the conventional HFPNN exploits the extended group method of data handling (GMDH) with some essential parameters of the network being provided by the designer and kept fixed throughout the overall development process. This restriction may hamper a possibility of producing an optimal architecture of the model. The augmented gHFPNN results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one we encounter in the conventional HFPNN. The GA-based design procedure being applied at each layer of HFPNN leads to the selection of preferred nodes (FPNs or PNs) available within the HFPNN. In the sequel, two general optimization mechanisms are explored. First, the structural optimization is realized via GAs whereas the ensuing detailed parametric optimization is carried out in the setting of a standard least square method-based learning. The performance of the gHFPNN is quantified through experimentation where we exploit data coming from processes of pH neutralization and NOx emission. These datasets have already been used quite intensively in fuzzy and neurofuzzy modeling. The obtained results demonstrate superiority of the proposed networks over the existing fuzzy and neural models. [Copyright &y& Elsevier]

Abstract: In this study, we introduce a concept of self-organizing neurofuzzy networks (SONFN), a hybrid modeling architecture combining relation-based neurofuzzy networks (NFN) and self-organizing polynomial neural networks (PNN). For such networks we develop a comprehensive design methodology and carry out a series of numeric experiments using data coming from the area of software engineering. The construction of SONFNs exploits fundamental technologies of computational intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms. The architecture of the SONFN results from a synergistic usage of NFN and PNN. NFN contributes to the formation of the premise part of the rule-based structure of the SONFN. The consequence part of the SONFN is designed using PNNs. We discuss two types of SONFN architectures with the taxonomy based on the NFN scheme being applied to the premise part of SONFN and propose a comprehensive learning algorithm. It is shown that this network exhibits a dynamic structure as the number of its layers as well as the number of nodes in each layer of the SONFN are not predetermined (as this is usually the case for a popular topology of a multilayer perceptron). The experimental results deal with well-known software data such as the NASA dataset concerning software cost estimation and the one describing software modules of the medical imaging system (MIS). In comparison with the previously discussed approaches, the self-organizing networks are more accurate and exhibit superb generalization capabilities. [Copyright &y& Elsevier]

Experimental software data sets describing software projects in terms of their complexity and development time have been a subject of intensive modeling. A number of various modeling methodologies and modeling designs have been proposed including neural networks, fuzzy, and neurofuzzy models. In this study, we introduce a concept of Self-organizing neurofuzzy networks (SONFN), a hybrid modeling architecture combining neurofuzzy networks (NFN) and polynomial neural networks (PNN). The development of the SONFN dwells on the technologies of Computational Intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms. The architecture of the SONFN results from a synergistic usage of neurofuzzy networks (NFNs) and polynomial neural networks (PNNs). NFNs contribute to the formation of the premise part of the rule-based structure of the SONFN. The consequence part of the SONFN is designed using PNNs. We discuss two classes of SONFN architectures and propose comprehensive learning algorithms. The experimental results include well-known software data such as the NASA data set concerning software cost estimation and the one describing software modules of the Medical Imaging System (MIS). [Copyright &y& Elsevier]

In this study, we introduce and investigate a class of neural architectures of polynomial neural networks (PNNs), develop a comprehensive design methodology and carry out a series of numeric experiments. PNN is a flexible neural architecture whose structure (topology) is developed through learning. In particular, the number of layers of the PNN is not fixed in advance but is generated on the fly. In this sense, PNN is a self-organizing network. We distinguish between two kinds of SOPNN architectures, that is, (a) polynomial neuron (PN) based and (b) fuzzy polynomial neuron (FPN) based self-organizing networks. This taxonomy is based on the character of each neuron structure in the network. Each of them comes with two structures referred here to as basic and the modified topology. Moreover, for each topology of the SOPNN we identify two types that is a generic and advanced type. The essence of the design procedure of self-organizing polynomial neural networks (SOPNN) dwells on the group method of data handling (GMDH) (IEEE Trans. Systems Man and Cybernet. 12 (1971) 364). Each node of the PN based SOPNN exhibits a high level of flexibility and realizes a polynomial type of mapping (linear, quadratic, and cubic) between input and output variables. FPN based SOPNN dwells on the ideas of fuzzy rule-based computing and neural networks. Especially in FPN based SOPNN, the generic rules in the system assume the form “if A then y = P(x)” where A is a fuzzy relation in the condition space while P(x) is a polynomial forming a conclusion part of the rule. Each FPN (processing element) consists of a series of the nonlinear inference rules. The conclusion part of the rules, especially the regression polynomial uses several types of high-order polynomials such as linear, quadratic, modified quadratic, and cubic. As the premise part of the rules, both triangular and Gaussian-like membership functions are studied. Simulations involve a series of synthetic as well as experimental data used across various neurofuzzy systems. A detailed comparative analysis is included as well. [Copyright &y& Elsevier]