Taylor and Bi-local Piecewise Approximations with Neuro-Fuzzy Systems

Methods of local approximations based on truncated Taylor series are well understood; several methods to compute bounds for the approximation errors are available (Christensen and Christensen, 2006), (Powell, 1981), (Shahriari, 2006). The use of Taylor approximations is convenient, among others, because methods to determine the approximation accuracy are well established. Taylor approximations are widely used in solving differential equations (Kloeden, Platen, 1995), (Tachev, 2009), control applications (Hedjar et al., 2005), circuit modeling (Jridi and Alfalou, 2009), data processing, image generation, signal prediction (Hedjar et al., 2005), and economic modeling (Judd, 1998).