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.