Optimised PWL recursive approximation and its application to neuro-fuzzy systems

In this work, a piecewise-linear (PWL) function approximation is described by a lattice algebra. The maximum (∨) and minimum (∧) lattice operators have been modified to incorporate interpolation capability of generated PWL function vertexes. As a result of that, a new recursive method called centred recursive interpolation (CRI) based on such operators is proposed and analysed for successive function smoothing and more accurate approximation. The resultant computational scheme is accurate but simple, as few parameters are needed for function definition. The method is tested by applying it to the optimum approximation of some sample functions, and it turns out to be a natural quadratic approximation. Due to its advantageous characteristics and the properties that Gaussian-like function based neuro-fuzzy systems show, optimised approximation of programmable Gaussian functions has been studied in detail. A table of optimum parameters has been obtained for approximating the function through different design schemes. This constitutes a previous theoretical work for the future hardware implementation of function generators in neuro-fuzzy systems.