Second-order Takagi-Sugeno model to identify sea water optically active constituent concentrations from Meris data

Several papers have demonstrated that Takagi-Sugeno models with linear functions as rule consequences are universal approximators. This theoretical result is practically achievable only if no constrain is enforced on the number of rules. Most of the methods proposed in the literature to build TS models, however, determine the number of rules based on the distribution of the known patterns on the input-output space, without taking the approximation error into account. Once the number of rules is fixed, the desired error could be not achievable. Using a real modeling application, namely, the identification of sea water optically active constituent concentrations from a set of measures of average subsurface reflectances over spectral channels centered around prefixed wavelength of a MEdium Resolution Imaging Spectrometer (MERIS) on board a satellite, we show that, once fixed the number of rules, the approximation error can be improved by using more complex, for instance quadratic, consequent functions rather than linear.