Simplified Approximations to Surfaces using Multiresolution Analysis and TSK Systems

A method for the construction of first order Takagi-Sugeno-Kang (TSK) systems with two input variables is described. The whole process is driven by the information provided by the wavelet transform and one parameter which represents the desired precision. The proposed algorithm uses that information to iteratively refine a partition of the universe of discourse and simplify the target function accordingly. As a result, the regions in which a coarser representation of the surface is acceptable in terms of precision loss are discovered. The final TSK system is constructed using the information gathered and provides a simple model wherever possible and a complex one only in those regions where precision demands it.