Design of Fuzzy Set-Based Polynomial Neural Networks with the Aid of Symbolic Encoding and Information Granulation

Abstract

In this paper, we introduce fuzzy-neural networks– Fuzzy Polynomial Neural Networks (FPNN) with fuzzy set-based polynomial neurons (FSPN) whose fuzzy rules include the information granules (about the real system) obtained through Information Granulation. We have developed a design methodology (genetic optimization using Genetic Algorithms) to find the optimal structure for fuzzy-neural networks that expanded from Group Method of Data Handling (GMDH). It is 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 that are the parameters of FPNN fixed by aid of genetic optimization that has search capability to find the optimal solution on the solution space. We adopt fuzzy set-based fuzzy rules as substitute for fuzzy relation-based fuzzy rules and apply the concept of Information Granulation to the proposed fuzzy set-based rules. The performance of genetically optimized FPNN (gFPNN) with fuzzy set-based polynomial neurons (FSPN) composed of fuzzy set-based rules is quantified through experimentation where we use a number of modeling benchmarks data which are already experimented with in fuzzy or neurofuzzy modeling.