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Abstract: In this study, we are concerned with a construction of granular neural networks (GNNs)—architectures formed as a direct result reconciliation of results produced by a collection of local neural networks constructed on a basis of individual data sets. Being cognizant of the diversity of the results produced by the collection of networks, we arrive at the concept of granular neural network, producing results in the form of information granules (rather than plain numeric entities) that become reflective of the diversity of the results generated by the contributing networks. The design of a granular neural network exploits the concept of justifiable granularity. Introduced is a performance index quantifying the quality of information granules generated by the granular neural network. This study is illustrated with the aid of machine learning data sets. The experimental results provide a detailed insight into the developed granular neural networks. [Copyright &y& Elsevier]

Abstract: In this study, we concentrate on the fundamentals and essential development issues of logic-driven constructs of fuzzy neural networks. These networks, referred to as logic-oriented neural networks, constitute an interesting conceptual and computational framework that greatly benefits from the establishment of highly synergistic links between the technology of fuzzy sets (or granular computing, being more general) and neural networks. The most essential advantages of the proposed networks are twofold. First, the transparency of neural architectures becomes highly relevant when dealing with the mechanisms of efficient learning. Here the learning is augmented by the fact that domain knowledge could be easily incorporated in advance prior to any learning. This becomes possible given the compatibility between the architecture of the problem and the induced topology of the neural network. Second, once the training has been completed, the network can be easily interpreted and thus it directly translates into a series of truth-quantifiable logic expressions formed over a collection of information granules. The design process of the logic networks synergistically exploits the principles of information granulation, logic computing and underlying optimization including those biologically inspired techniques (such as particle swarm optimization, genetic algorithms and alike). We elaborate on the existing development trends, present key methodological pursuits and algorithms. In particular, we show how the logic blueprint of the networks is supported by the use of various constructs of fuzzy sets including logic operators, logic neurons, referential operators and fuzzy relational constructs. [Copyright &y& Elsevier]

In this paper, we present a new granular classifier in two versions (iterative and non–iterative), by adopting some ideas originating from a kind of Functional Link Artificial Neural Network and the Functional Network schemes. These two architectures are substantially the same: they both use a function basis instead of the usual activation function, but they are different for the learning algorithm. We augment them from the perspective of Granular Computing and information granules, designing a new kind of classifier and two learning algorithms, by taking into account granularity of information. The proposed classifier exhibits the advantages of the granular architectures, that is higher accuracy and transparency. We formally discuss the convergence of the iterative learning scheme. We carry out some numerical experiments using publicly available data, by comparing the results against those results produced by the state-of-the-art methods. In particular, we achieved sound results by invoking the iterative learning scheme. [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]

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 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]