A Novel Interval Type-2 Fuzzy System Identification Method Based on the Modified Fuzzy C-Regression Model

In this article, a novel interval type-2 Takagi–Sugeno fuzzy $c$ -regression modeling method with a modified distance definition is proposed. The modified distance definition is developed to describe the distance between each data point and the local type-2 fuzzy model. To improve the robustness of the proposed identification method, a modified objective function is presented. In addition, different from most previous studies that require numerous free parameters to be determined, an interval type-2 fuzzy $c$ -regression model is developed to reduce the number of such free parameters. Furthermore, an improved ratio between the upper and lower weights is proposed based on the upper and lower membership function with each input data, and the ordinary least-squares method is adopted to establish the type-2 fuzzy model. The Box–Jenkins model and two numerical models are given to illustrate the effectiveness and robustness of the proposed results.

I. Introduction

Most real-world physical and engineering systems are nonlinear. In general, an analysis of a nonlinear system is more difficult to achieve than that of a linear system; therefore, the system identification problem has become a popular research topic. During the past few decades, fuzzy techniques have been successfully applied in the prediction [1], [2]; analysis of control synthesis [3], [4]; identification; and pattern recognition. The Takagi–Sugeno (T–S) fuzzy-model-based identification approach is regarded as a systematic and effective method for dealing with the system identification problem of a nonlinear system. It includes numerous local models that are described as a set of fuzzy IF-THEN rules to represent the local linear input–output relationship for the system. By blending these submodels with fuzzy membership functions, the overall T–S fuzzy model can be established to represent a nonlinear model and accurately describe an uncertain system and a nonlinear model. Due to these advantages, many studies use the T–S fuzzy model for solving the system identification problem [2], [5]. Identification problems based on the T–S fuzzy model are divided into two categories, namely: 1) dynamic system identification, for which most system parameters have to be known in advance and 2) the establishment of the T–S fuzzy model using the input–output data. In general, the latter is more suitable for the system identification for which there are unknown parameters. Various identification methods have been developed based on the input–output data [2], [6]–[8].