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.     

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).     

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.     

Evaluation of performance and service life of low pressure lPG regulators for home use

This paper presents the evaluation of LPG (Liquefied petroleum gas) regulators for home use. For the evaluation, several properties of the regulators were experimentally analyzed, such as the operation of safety device, the adjusting and lock-up pressure, the adjusting spring and the diaphragm, with respect to the used time of the regulators. Experimental results showed that the initial operation performances of regulators were degraded with increase of the service time and also showed that the degradation of the performance and material property could become serious after about six-year-use of the regulators.     

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.     

Fuzzy linear regression based on Polynomial Neural Networks

In this study, we introduce an estimation approach to determine the parameters of the fuzzy linear regression model. The analytical solution to estimate the values of the parameters has been studied. The issue of negative spreads of fuzzy linear regression makes the problem to be NP complete. To deal with this problem, an iterative refinement of the model parameters based on the gradient decent optimization has been introduced.In the proposed approach, we use a hierarchical structure which is composed of dynamically accumulated simple nodes based on Polynomial Neural Networks the structure of which is very flexible.In this study, we proposed a new methodology of fuzzy linear regression based on the design method of Polynomial Neural Networks. Polynomial Neural Networks divide the complicated analytical approach to estimate the parameters of fuzzy linear regression into several simple analytic approaches.The fuzzy linear regression is implemented by Polynomial Neural Networks with fuzzy numbers which are formed by exploiting clustering and Particle Swarm Optimization. It is shown that the design strategy produces a model exhibiting sound performance.