PWL Approximation of Non-linear Functions for the Implementation of Neuro-Fuzzy Systems

A piecewise linear (PWL) function approximation scheme is described by a lattice algebra of modified operators that allows for the interpolation of PWL function vertexes. A new recursive method called Centred Recursive Interpolation (CRI) based on such modified operators is analysed for successive function smoothing and more accurate approximation. This approximation method, simple but accurate as few parameters are needed for function definition, turns out to be a natural quadratic approximation. Due to the properties that neuro-fuzzy systems with gaussian-like non-linear functions show, CRI is applied to the approximation of a sample gaussian function with width control. Computational simplicity and parameter programmability have been central objectives. As PWL functions are generated by means of lattice operators in a recursive manner, this approximation method is particularly suitable for hardware implementation of function generation circuits. Key-Words: neuro-fuzzy system, PWL function, lattice operator, recursive linear interpolation, membership function, gaussian function, function generation circuit.