Function approximation with polynomial membership functions and alternating cluster estimation
type: Item
instance of: scholarly article
title: Function approximation with polynomial membership functions and alternating cluster estimation
zbMATH Open document ID: 0932.65076
DOI: 10.1016/S0165-0114(98)00164-X
author: Thomas A. Runkler
author: James C. Bezdek
published in: Fuzzy Sets and Systems
publication date: 2000-03-15T00:00:00Z
review text: Nonlinear functions can be approximated by local linear models, for instance by a first-order Takagi-Sugeno model with membership function \(\mu_i(x)\) and linear right-hand side functions \(f_i(x)= m_i(x- x_i)+ y_i\) \((i= 1,\dots, c)\). Since piecewise linear membership functions lead to nondifferentiable input-output characteristics, the authors compute piecewise quadratic membership functions \(\mu_i(x)\) for a differentiable, minimal-order piecewise polynomial approximation. The parameters \(x_i\), \(y_i\) and \(m_i\) are obtained by fuzzy \(c\)-elliptotypes alternating optimization or alternating cluster estimation. In numerical tests the best approximation results are obtained with piecewise quadratic membership functions and alternating cluster estimation.
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 93C42
Mathematics Subject Classification ID: 65D10
zbMATH DE Number: 1328235
zbMATH Keywords: fuzzy system
zbMATH Keywords: first-order Takagi-Sugeno model
zbMATH Keywords: function approximation
zbMATH Keywords: piecewise quadratic membership function
zbMATH Keywords: alternating cluster estimation
zbMATH Keywords: fuzzy control
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1328235