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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]

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]