Function approximation with polynomial membership functions and alternating cluster estimation

✍ Scribed by Thomas A. Runkler; James C. Bezdek

• Book ID: 104292919
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 613 KB
• Volume: 101
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(98)00164-x

✦ Synopsis

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. @