Self-organizing neurofuzzy networks based on evolutionary fuzzy granulation

Experimental software datasets 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 such development frameworks as 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). For these networks we develop a comprehensive design methodology. The construction of SONFNs takes advantage of the well-established technologies of computational intelligence (CI), namely fuzzy sets, neural networks and genetic algorithms. The architecture of the SONFN results from a synergistic usage of NFNs and PNNs. 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 whose taxonomy is based on the NFN scheme being applied to the premise part of SONFN. We introduce 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 the case in a popular topology of a multilayer perceptron). The experimental results include a well-known NASA dataset concerning software cost estimation.     

Genetically optimized fuzzy polynomial neural networks with fuzzy set-based polynomial neurons

In this paper, we propose and investigate a new category of neurofuzzy networks—fuzzy polynomial neural networks (FPNN) endowed with fuzzy set-based polynomial neurons (FSPNs) We develop a comprehensive design methodology involving mechanisms of genetic optimization, and genetic algorithms (GAs) in particular. The conventional FPNNs developed so far are based on the mechanisms of self-organization, fuzzy neurocomputing, and evolutionary optimization. The design of the network exploits the FSPNs as well as the extended group method of data handling (GMDH). Let us stress that in the previous development strategies some essential parameters of the networks (such as the number of input variables, the order of the polynomial, the number of membership functions, and a collection of the specific subset of input variables) being available within the network are provided by the designer in advance and kept fixed throughout the overall development process. This restriction may hamper a possibility of developing an optimal architecture of the model. The design proposed in this study addresses this issue. The augmented and genetically developed FPNN (gFPNN) results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one we encounter in the conventional FPNNs. The GA-based design procedure being applied at each layer of the FPNN leads to the selection of the most suitable nodes (or FSPNs) available within the FPNN. 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 gFPNN is quantified through experimentation in which we use a number of modeling benchmarks—synthetic and experimental data being commonly used in fuzzy or neurofuzzy modeling. The obtained results demonstrate the superiority of the proposed networks over the models existing in the references.     

ReNFFor: a recurrent neurofuzzy forecaster for telecommunications data

In this work, a dynamic neurofuzzy system for forecasting outgoing telephone calls in a University Campus is proposed. The system comprises modified Takagi–Sugeno–Kang fuzzy rules, where the rules’ consequent parts are small neural networks with unit internal recurrence. The characteristics of the proposed forecaster, which is entitled recurrent neurofuzzy forecaster, are depicted via a comparative analysis with a series of well-known forecasting models.     

Hybrid fuzzy set-based polynomial neural networks and their development with the aid of genetic optimization and information granulation

We introduce a new architecture of feed-forward neural networks called hybrid fuzzy set-based polynomial neural networks (HFSPNNs) that are composed of heterogeneous feed-forward neural networks such as polynomial neural networks (PNNs) and fuzzy set-based polynomial neural networks (FSPNNs). We develop their comprehensive design methodology by embracing mechanisms of genetic optimization and information granulation. The construction of information granulation-driven HFSPNN exploits fundamental technologies of computational intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms (GAs). The architecture of the resulting information granulation-driven genetically optimized HFSPNN results from a synergistic usage of the hybrid system generated by combining original fuzzy set-based polynomial neurons (FSPNs)-based FSPNN with polynomial neurons (PNs)-based PNN. The design of the conventional genetically optimized HFPNN exploits the extended Group Method of Data Handling (GMDH) whose some essential parameters of the network being tuned with the use of genetic algorithms throughout the overall development process. Two general optimization mechanisms are explored. First, the structural optimization is realized via GAs while the ensuing detailed parametric optimization is carried out in the setting of a standard least square method-based learning. The performance of the gHFSPNN is quantified through extensive experimentation where we considered a number of modeling benchmarks (synthetic and experimental data already experimented with in fuzzy or neurofuzzy modeling).     

关系结构中的神经计算

人工神经网络在许多应用领域中建立了一种新的高度并行计算的结构。具有表示概念和知识的模糊集合被认为是处理人们日常生活中不确定问题的一种工具。特别是关系结构,它在构造现实世界中的形式关系模型中起着非常重要的作用。本文根据模糊集合理论,提出新的神经网络结构及其新的学习算法,并研究其性质。一方面把模糊集合的方法学应用于神经网络结构和学习算法的研究,同时使得神经网络的硬件实现更加容易。     

Advanced self-organizing polynomial neural network

In this paper, we introduce a concept of advanced self-organizing polynomial neural network (Adv_SOPNN). The SOPNN is a flexible neural architecture whose structure is developed through a modeling process. But the SOPNN has a fatal drawback; it cannot be constructed for nonlinear systems with few input variables. To relax this limitation of the conventional SOPNN, we combine a fuzzy system and neural networks with the SOPNN. Input variables are partitioned into several subspaces by the fuzzy system or neural network, and these subspaces are utilized as new input variables to the SOPNN architecture. Two types of the advanced SOPNN are obtained by combining not only the fuzzy rules of a fuzzy system with SOPNN but also the nodes in a hidden layer of neural networks with SOPNN into one methodology. The proposed method is applied to the nonlinear system with two inputs, which cannot be identified by conventional SOPNN to show the performance of the advanced SOPNN. The results show that the proposed method is efficient for systems with limited data set and a few input variables and much more accurate than other modeling methods with respect to identification error.     

An Experimental Study on Nonlinear Function Computation for Neural/Fuzzy Hardware Design

An experimental study on the influence of the computation of basic nodal nonlinear functions on the performance of (NFSs) is described in this paper. Systems' architecture size, their approximation capability, and the smoothness of provided mappings are used as performance indexes for this comparative paper. Two widely used kernel functions, the sigmoid-logistic function and the Gaussian function, are analyzed by their computation through an accuracy-controllable approximation algorithm designed for hardware implementation. Two artificial neural network (ANN) paradigms are selected for the analysis: backpropagation neural networks (BPNNs) with one hidden layer and radial basis function (RBF) networks. Extensive simulation of simple benchmark approximation problems is used in order to achieve generalizable conclusions. For the performance analysis of fuzzy systems, a functional equivalence theorem is used to extend obtained results to fuzzy inference systems (FISs). Finally, the adaptive neurofuzzy inference system (ANFIS) paradigm is used to observe the behavior of neurofuzzy systems with learning capabilities     

A fuzzy ensemble of parallel polynomial neural networks with information granules formed by fuzzy clustering

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.     

Variable selection algorithm for the construction of MIMO operatingpoint dependent neurofuzzy networks

An input variable selection procedure is introduced for the identification and construction of multi-input multi-output (MIMO) neurofuzzy operating point dependent models. The algorithm is an extension of a forward modified Gram-Schmidt orthogonal least squares procedure for a linear model structure which is modified to accommodate nonlinear system modeling by incorporating piecewise locally linear model fitting. The proposed input nodes selection procedure effectively tackles the problem of the curse of dimensionality associated with lattice-based modeling algorithms such as radial basis function neurofuzzy networks, enabling the resulting neurofuzzy operating point dependent model to be widely applied in control and estimation. Some numerical examples are given to demonstrate the effectiveness of the proposed construction algorithm     

Predicting Chaotic Time Series Using Neural and Neurofuzzy Models: A Comparative Study

The prediction accuracy and generalization ability of neural/neurofuzzy models for chaotic time series prediction highly depends on employed network model as well as learning algorithm. In this study, several neural and neurofuzzy models with different learning algorithms are examined for prediction of several benchmark chaotic systems and time series. The prediction performance of locally linear neurofuzzy models with recently developed Locally Linear Model Tree (LoLiMoT) learning algorithm is compared with that of Radial Basis Function (RBF) neural network with Orthogonal Least Squares (OLS) learning algorithm, MultiLayer Perceptron neural network with error back-propagation learning algorithm, and Adaptive Network based Fuzzy Inference System. Particularly, cross validation techniques based on the evaluation of error indices on multiple validation sets is utilized to optimize the number of neurons and to prevent over fitting in the incremental learning algorithms. To make a fair comparison between neural and neurofuzzy models, they are compared at their best structure based on their prediction accuracy, generalization, and computational complexity. The experiments are basically designed to analyze the generalization capability and accuracy of the learning techniques when dealing with limited number of training samples from deterministic chaotic time series, but the effect of noise on the performance of the techniques is also considered. Various chaotic systems and time series including Lorenz system, Mackey-Glass chaotic equation, Henon map, AE geomagnetic activity index, and sunspot numbers are examined as case studies. The obtained results indicate the superior performance of incremental learning algorithms and their respective networks, such as, OLS for RBF network and LoLiMoT for locally linear neurofuzzy model.     

Feature space mapping as a universal adaptive system

The most popular realizations of adaptive systems are based on the neural network type of algorithms, in particular feedforward multilayered perceptrons trained by backpropagation of error procedures. In this paper an alternative approach based on multidimensional separable localized functions centered at the data clusters is proposed. In comparison with the neural networks that use delocalized transfer functions this approach allows for full control of the basins of attractors of all stationary points. Slow learning procedures are replaced by the explicit construction of the landscape function followed by the optimization of adjustable parameters using gradient techniques or genetic algorithms. Retrieving information does not require searches in multidimensional subspaces but it is factorized into a series of one-dimensional searches. Feature Space Mapping is applicable to learning not only from facts but also from general laws and may be treated as a fuzzy expert system (neurofuzzy system). The number of nodes (fuzzy rules) is growing as the network creates new nodes for novel data but the search time is sublinear in the number of rules or data clusters stored. Such a system may work as a universal classificator, approximator and reasoning system. Examples of applications for the identification of spectra (classification), intelligent databases (association) and for the analysis of simple electrical circuits (expert system type) are given.     

Neural and Neurofuzzy FELA Adaptive Robot Control Using Feedforward and Counterpropagation Networks

In this paper, the application of neural networks and neurofuzzy systems to the control of robotic manipulators is examined. Two main control structures are presented in a comparative manner. The first is a Counter Propagation Network-based Fuzzy Controller (CPN-FC) which is able to self-organize and correct on-line its rule base. The self-tuning capability of the fuzzy logic controller is attained by taking advantage of the structural equivalence between the fuzzy logic controller and a counterpropagation network. The second control structure is a more familiar neural adaptive controller based on a feedforward (MLP) network. The neural controller learns the inverse dynamics of the robot joints, and gradually eliminates the model uncertainties and disturbances. Both schemes cooperate with the computed torque control algorithm, and in that way the reduction of their complexity is achieved. The ability of adaptive fuzzy systems to compete with neural networks in difficult control problems is demonstrated. A sufficient set of numerical results is included.     

Structure selection of neurofuzzy networks based on support vector regression

Neurofuzzy networks are being used increasingly to model non-linear dynamic systems, since they have the approximating ability of neural networks and the transparency of fuzzy systems. However, good generalization results can only be obtained if the structure of the network is suitably chosen. It is shown here that the structure of neurofuzzy networks with scatter partitioning can be obtained from the support vectors (SV) of the Support Vector Regression (SVR), since the SVR can be transformed to a neurofuzzy network. The main advantage of this approach is that the structure of the neurofuzzy networks can now be objectively chosen, as the SV are obtained by constrained optimization for a given modelling error bound. Since neurofuzzy networks are linear-inweights networks, the estimate of the weights of the networks can be obtained by the linear least-squares method. The properties of neurofuzzy networks based on the SV are derived, and its performance is illustrated by a simulation example involving a nonlinear system, and the modeling of Southern Oscillation Index.     

Neurofuzzy identification of an autonomous underwater vehicle

Neurofuzzy modelling is ideally suited to many nonlinear system identification and data modelling applications. By combining the attractive attributes of fuzzy systems and neural networks transparent models of ill-defined systems can be identified. Available expert a priori knowledge is used to construct an initial model. Data modelling techniques from the neural network, statistical and conventional system identification communities are then used to adapt these models. As a result accurate parsimonious models which are transparent and easy to validate are identified. Recent advances in the datadriven identification algorithms have now made neurofuzzy modelling appropriate for high-dimensional problems for which the expert knowledge and data may be of a poor quality. In this paper neurofuzzy modelling techniques are presented. This powerful approach to system identification is demonstrated by its application to the identification of an Autonomous Underwater Vehicle (AUV).     

IG-based genetically optimized fuzzy polynomial neural networks with fuzzy set-based polynomial neurons

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.     

Numerical solution of a system of fuzzy polynomials by fuzzy neural network

In this paper, a new approach for solving systems of fuzzy polynomials based on fuzzy neural network (FNN) is presented. This method can also lead to improve numerical methods. In this work, an architecture of fuzzy neural networks is also proposed to find a real root of a system of fuzzy polynomials (if exists) by introducing a learning algorithm. Finally, we illustrate our approach by numerical examples.     

A neurofuzzy methodology for impedance-based multiphase flow identification

A neurofuzzy methodology for flow identification based on signals obtained from an impedance void meter is presented. The methodology combines the filtering and interpolative capabilities of neural networks with the representational advantages of fuzzy systems for the purpose of mapping idiosyncratic area-averaged impedance measurements to multiphase flow regimes. It has been shown that electrical signals representing the conductance of the intervening medium can be used to infer crucial flow parameters, and that area-averaged signals contain sufficient information about flow regime and the structure of its two-phase constituents. The neurofuzzy approach is a promising means for reconstructing the visual imagery of flow in a process, analogous to tomography, and holds considerable promise for multiphase flow diagnostic and measurement applications in the nuclear as well as in the petroleum, biomedical, and food-processing industries.     

模糊神经网络在高强混凝土强度预测与配合比设计中的应用

针对模糊系统中规则结论为数值和线性函数的两种表示方式 ,找到了它们的共同点 ,将它们置于同一网络结构中 ,形成规则结论为数值和线性函数 (T -S模型 )的两种模糊神经网络 (FuzzyNeuralNetworks,简称FNN) ,导出了它们的网络模型及其学习算法。并首次将其应用于高强混凝土强度预测和配合比设计中。文章还介绍了一种简单有效地从样本数据中提取模糊规则及确定FNN参数初值的方法。运算结果表明 ,FNN不仅具有很高的预测精度 ,而且网络的结点和权值均具有明确的物理意义 ,可以借此深入分析高强混凝土综合性能与影响它们的因素之间的非线性关系     

Polynomial neural networks architecture: analysis and design

In this study, we introduce and investigate a class of neural architectures of Polynomial Neural Networks (PNNs), discuss a comprehensive design methodology and carry out a series of numeric experiments. Two kinds of PNN architectures, namely a basic PNN and a modified PNN architecture are discussed. Each of them comes with two types such as the generic and the advanced type. The essence of the design procedure dwells on the Group Method of Data Handling. PNN is a flexible neural architecture whose structure is developed through learning. In particular, the number of layers of the PNN is not fixed in advance but becomes dynamically meaning that the network grows over the training period. In this sense, PNN is a self-organizing network. A comparative analysis shows that the proposed PNN are models with higher accuracy than other fuzzy models.     

基于模糊神经网络的专家系统及应用

专家系统前景广阔，但其进一步发展必须引入其他先进技术，神经网络和模糊系统是解决知识获和经验性知识的不确定性等传统专家系统的“瓶颈”问题的全新途径。