Fuzzy Radial Basis Function Neural Networks with information granulation and its parallel genetic optimization

  • Authors:

  • Sung-Kwun Oh;Wook-Dong Kim;Witold Pedrycz;Kisung Seo

  • Affiliations:

  • Department of Electrical Engineering, The University of Suwon, San 2-2 Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, South Korea;Department of Electrical Engineering, The University of Suwon, San 2-2 Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, South Korea;Department of Electrical & Computer Engineering, University of Alberta, Edmonton T6R 2V4 AB, Canada and Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz Un ...;Department of Electronic Engineering, Seokyeong University, Jungneung-Dong 16-1, Sungbuk-Gu, Seoul 136-704, South Korea

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2014

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Abstract

Fuzzy modeling of complex systems is a challenging task, which involves important problems of dimensionality reduction and calls for various ways of improving the accuracy of modeling. The IG-FRBFNN, a hybrid architecture of the IG-FIS (Fuzzy Inference System) and FRBFNN (Fuzzy Radial Basis Function Neural Networks), is proposed to address these problems. The paper is concerned with the analysis and design of IG-FRBFNNs and their optimization by means of the Hierarchical Fair Competition-based Parallel Genetic Algorithm (HFC-PGA). In the proposed network, the membership functions of the premise part of the fuzzy rules of the IG-based FRBFNN model directly rely on the computation of the relevant distance between data points and the use of four types of polynomials such as constant, linear, quadratic and modified quadratic are considered for the consequent part of fuzzy rules. Moreover, the weighted Least Square (WLS) learning is exploited to estimate the coefficients of the polynomial forming the conclusion part of the rules. Since the performance of the IG-RBFNN model is affected by some key design parameters, such as a specific subset of input variables, the fuzzification coefficient of the FCM, the number of rules, and the order of polynomial of the consequent part of fuzzy rules, it becomes beneficial to carry out both structural as well as parametric optimization of the network. In this study, the HFC-PGA is used as a comprehensive optimization vehicle. The performance of the proposed model is illustrated by means of several representative numerical examples.