An Adaptive Fuzzy Wavelet Network with Gradient Learning for Nonlinear Function Approximation

Oysal Y., Yilmaz S.

JOURNAL OF INTELLIGENT SYSTEMS, cilt.23, sa.2, ss.201-212, 2014 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 23 Sayı: 2
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1515/jisys-2013-0068
  • Dergi Adı: JOURNAL OF INTELLIGENT SYSTEMS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.201-212
  • Anahtar Kelimeler: Wavelet neural networks, ANFIS, fuzzy systems, time series prediction
  • Anadolu Üniversitesi Adresli: Evet

Özet

In this article, a new adaptive fuzzy wavelet neural network (AFWNN) model is proposed for nonlinear function approximation problems. The AFWNN model is based on the traditional Takagi-Sugeno-Kang fuzzy system. Specifically, this model replaces the membership functions of fuzzy rules with wavelet basis functions, which are known to have time and frequency localization properties, i.e., they can approximate patterns both in the time and frequency domains. The structure of the AFWNN model is derived from that of the adaptive neuro-fuzzy inference system (ANFIS). However, the AFWNN improves over the ANFIS by replacing Gaussian functions in the hidden layer with wavelet basis functions. The AFWNN model is trained using a gradient-based optimization algorithm. The AFWNN is then tested on three function approximation problems of time series prediction. For certain types of nonlinear time series, for instance fractal processes, the AFWNN is found to be substantially more accurate than alternative methods.