A Design of Genetically Oriented Fuzzy Relation Neural Networks (FrNNs) Based on the Fuzzy Polynomial Inference Scheme

Abstract

In this paper, we introduce new architectures of genetically oriented fuzzy relation neural networks (FrNNs) and offer a comprehensive design methodology that supports their development. The proposed FrNNs are based on ldquoif-thenrdquo-rule-based networks, with the extended structure of the premise and the consequence parts of the individual rules. We consider two types of the FrNN topologies, which are called FrNN-I and FrNN-II here, depending upon the usage of inputs in the premise and the consequence of fuzzy rules. Three different forms of regression polynomials (namely, constant, linear, and quadratic) are used to construct the consequence of the rules. In order to develop optimal FrNNs, the structure and the parameters are optimized using genetic algorithms (GAs). The proposed methodology is compared when the two development strategies, with separate and simultaneous optimization schemes that involve structure and parameters, are carried out. Given the large search space associated with these FrNN models, we enhance the search capabilities of the GAs by introducing the dynamic variants of genetic optimization. It fully exploits the processing capabilities of the FrNNs by supporting their structural and parametric optimization. To evaluate the performance of the proposed FrNNs, we exploit a suite of several representative numerical examples. A comparative analysis shows that the FrNNs exhibit higher accuracy and predictive capabilities as well as better modeling stability, when compared with some other models that exist in the literature.