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• 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]

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 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 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 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 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]