Identifying Rule-Based TSK Fuzzy Models

ABSTRACT: This article presents a rule-based fuzzy model for the identification of nonlinear MISO (multiple input, single output) systems. The presented method of fuzzy modeling consists of two parts: (1) structure modeling, i.e., the determination of the number of rules and input variables involved respectively, and (2) parameter optimization, i.e., the optimization of the location and form of the curves which describe the fuzzy sets and the optimization of the consequence parameters. For structure modeling we use a modified TSK-model, which was first proposed by Takagi, Sugeno, and Kang in [Takagi 85, Sugeno 88]. For parameter optimization of the initial model we propose singular value decomposition (SVD). To optimize the parameters of further models we propose the use of RPROP [Riedmiller 93, Zell 94]. We applied RPROP to the modified version of the TSK-model, implemented the algorithm, and tested its performance [Männle 95, Männle 96]. In this article we focus on the structure modeling part. By means of two examples we show the performance of RPROP and the input space partitioning performed by the structuring algorithm.