On wavelet based enhancing possibilities of fuzzy classification methods

If the antecedents of a fuzzy classification method are derived from pictures or measured data, it might have too many dimensions to handle. A classification scheme based on such data has to apply a careful selection or processing of the measured results: either a sampling, re-sampling is necessary or the usage of functions, transformations that reduce the long, high dimensional observed data vector or matrix into a single point or to a low number of points. Wavelet analysis can be useful in such cases in two ways. As the number of resulting points of the wavelet analysis is approximately half at each filters, a consecutive application of wavelet transform can compress the measurement data, thus reducing the dimensionality of the signal, i.e., the antecedent. An SHDSL telecommunication line evaluation is used to demonstrate this type of applicability, wavelets help in this case to overcome the problem of a one dimensional signal sampling. In the case of using statistical functions, like mean, variance, gradient, edge density, Shannon or Rényi entropies for the extraction of the information from a picture or a measured data set, and they don not produce enough information for performing the classification well enough, one or two consecutive steps of wavelet analysis and applying the same functions for the thus resulting data can extend the number of antecedents, and can distill such parameters that were invisible for these functions in the original data set. We give two examples, two fuzzy classification schemes to show the improvement caused by wavelet analysis: a measured surface of a combustion engine cylinder and a colonoscopy picture. In the case of the first example the wear degree is to be determine, in the case of the second one, the roundish polyp content of the picture. In the first case the applied statistical functions are Rényi entropy differences, the structural entropies, in the second case mean, standard deviation, Canny filtered edge density, gradients and the entropies. In all the examples stabilized KH rule interpolation was used to treat sparse rulebases. The preliminary version of this paper was presented at the 3rd Conference on Information Technology, Systems Research and Computational Physics, 2–5 July 2018, Cracow, Poland [1].