Interval-valued membership function estimation for fuzzy modeling

Abstract

Fuzzy modeling is an important topic in fuzzy sets theory and applications. A powerful method for constructing an interval-valued Takagi–Sugeno fuzzy model (IVFM), based on input–output data of the identified system, is presented. In this investigation, a Takagi–Sugeno fuzzy model is automatically generated in three steps: (1) Structure identification, (2) Envelope detection and (3) parameters identification. In the structure identification phase, a clustering method based on Gustafson–Kessel algorithm is used in order to detect the linear subsystems of the whole nonlinear system (local linearization). Then, an envelope detection algorithm (EDA) based on derivative concept is proposed to estimate both the upper and lower functions of the interval-valued membership function defined point-wise. In the parameter identification step, the least squares algorithm is applied to compute the best parameter values of the premises (Gaussians) and the Kalman Filter algorithm to compute the consequences (straight lines) parameters. The effectiveness of this approach is demonstrated on approximating some nonlinear static functions, real world data and dynamical systems.