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

Horia-Nicolai TEODORESCU^1,2
¹ Institute of Computer Science of the Romanian Academy, Iaşi Branch,
11, Carol I Blvd., 700505, Iaşi, Romania

² Gheorghe Asachi Technical University of Iasi,
67, Dimitrie Mangeron Blvd., 700050, Iaşi, Romania,
hteodor@etti.tuiasi.ro

Abstract: A fuzzy neuron (linear combiner of fuzzy systems) with piecewise polynomial characteristic function is defined and analyzed. The linear fuzzy neuron uses a pre-specified type of fuzzy logic systems with complementary pairs of input membership functions. Taylor local approximations are built using the described fuzzy neuron. Moreover, local Taylor approximations are obtained using single fuzzy systems. Hence, the linear combiner fuzzy neurons are universal local approximators implementing truncated Taylor series. Moreover, they represent continuous piecewise approximators. Bi-local approximation with fuzzy logic systems are also introduced and demonstrated.

Keywords: Local approximation, TS system, fuzzy neuron, universal local approximator, approximation algorithm.

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CITE THIS PAPER AS:
H.-N. TEODORESCU, Taylor and Bi-local Piecewise Approximations with Neuro-Fuzzy Systems, Studies in Informatics and Control, ISSN 1220-1766, vol. 21 (4), pp. 367-376, 2012. https://doi.org/10.24846/v21i4y201202