Function approximation with polynomial membership functions and alternating cluster estimation

Fuzzy Sets and SystemsPublished 1 January 1999

Thomas A. Runkler, James C. Bezdek

DOI10.1016/s0165-0114(98)00164-x

Source URL

Citations36

SJR quartileQ1

SJR score0.75

SNIP1.25

TL;DR

A method to determine parameters of piecewise quadratic membership functions to obtain characteristics which exactly match the rule centers and the corresponding slopes is developed.

Abstract

Nonlinear functions are often approximated using local linear models. Sets of local linear models can be represented as a first-order Takagi Sugeno (TS) system. triangular and trapezoidal left-hand side membership functions are not compatible with TS systems because they lead to non-differentiable input-output characteristics. We develop a method to determine parameters of piecewise quadratic membership functions to obtain characteristics which exactly match the rule centers and the corresponding slopes. The right-hand side parameters are obtained using (i) fuzzy c-elliptotypes alternating optimization and (ii) alternating cluster estimation. In our experiments the smoothest and most accurate approximations are obtained with piecewise quadratic membership functions and alternating cluster estimation.

Keywords

Computer ScienceDecision Sciences

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