A global-local learning algorithm for identifying Takagi-Sugeno-Kang fuzzy models

The fuzzy inference system proposed by Takagi, Sugeno and Kang, which is known as the TSK model in fuzzy system literature, provides a powerful tool for modeling complex nonlinear systems. Unlike conventional modeling where a single model is used to describe the global behavior of a system, TSK modeling is essentially a multi-model approach in which simple submodels combined to describe the global behavior of the system. Most existing learning algorithms for identifying the TSK model are based on minimizing the square of the residual between the overall outputs of the real system and the identified model. Although these algorithms can generate a TSK model with good global performance, they cannot guarantee the resulting model to have a good local performance. Often, the submodels in the TSK model may exhibit an erratic local behavior which is difficult to interpret. Since one of the important motivations of using the TSK model is to gain insights into the model, it is important to investigate the interpretability issue of the TSK model. We propose a learning algorithm that integrates global learning and local learning in a single algorithmic framework. This algorithm uses the idea of local weighted regression and local approximation in nonparametric statistics, but remains the component of global fitting in the existing learning algorithms. The algorithm is capable of adjusting its parameters based on the user´s preference, generating models with good trade-off in terms of global fitting and local interpretation. We illustrate the performance of the proposed algorithm using a motorcycle crash modeling example