New Perspectives for the Integration of Wavelet Theory into Soft Computing

We review the main methods combining wavelet to soft computing. The integration of wavelet theory into soft computing started more than ten years ago, using wavelet analysis essentially as a preprocessing method. The first real integration of wavelet into soft computing coincided to the development of wavelet-networks. In the last three years, an increasing number of applications of wavelet-networks have been reported. The complementarity of fuzzy logic and multiresolution analysis has been also recognized. Successful applications of fuzzy-wavelet techniques in commercial products (flame detectors) have been carried out. At time, a number of emergent techiques show new perspectives for the integration of wavelet theory into soft computing. Fuzzy wave-nets is one of them, a technique integrating multiresolution into neurofuzzy. The integration of evolutionary computing in wavelet-based search algorithm, such as matching pursuits, is another promising research direction. Finally we show the great potential of wavelet-based techniques in the logarithmic domain in connection with the problem of decomposing a function as sums and products of simple basis functions.