A T–S Fuzzy Model Identification Approach Based on a Modified Inter Type-2 FRCM Algorithm

Hyper-plane-shaped clustering (HPSC) has been demonstrated to be more effective in Takagi-Sugeno (T-S) fuzzy model identification compared to hyper-sphere-shaped clustering. Although some HPSC algorithms, based on type-2 fuzzy theory, have already been developed and have been demonstrated to have outstanding performance in T-S fuzzy modeling, mismatching of the traditional hyper-sphere-shaped membership function and HPSC results will inevitably restrict the modeling performance. In this paper, a modified inter type-2 fuzzy c-regression model (IT2-FCRM) clustering and new hyper-plane-shaped Gaussian membership function were proposed for T-S fuzzy modeling. In the proposed approach, the coefficients of the upper and lower hyperplanes were deduced based on an IT2-FCRM algorithm. Then, a hyper-plane-shaped membership function was directly defined using the hyperplanes to identify the antecedent parameters of the T-S fuzzy model. The experimental results of several benchmark problems show that identification of T-S model accuracy was greatly promoted.

I. Introduction

Modeling techniques based on input–output data have been widely used to obtain an accurate model for a nonlinear system in many fields [1]– [4]. Fuzzy systems have shown excellent ability to describe the complicated dynamic of nonlinear behaviors of a dynamic process. Fuzzy model identification is an effective tool for high precision modeling of complicated nonlinear system based on measured data. With the nonlinear mapping capability of fuzzy logic, a complicated nonlinear system defined on a compact set can uniformly approximate any degree of accuracy [5]–[7]. Among the different types of fuzzy modeling approaches, the T–S fuzzy model proposed by Takagi and Sugeno is one of the most popular ones [8], [9]. The nature of the T–S model is to establish multiple local linear models to approximate the nonlinear system through fuzzy partitioning of input–output data of the nonlinear system and subsequent weighting of the local linear models [10]. T–S fuzzy model construction consists of two phrases, structure identification, and parameter identification [11].