Type-2 T-S fuzzy modeling for the dynamic systems with measurement noise

In actual industrial processes, the measurement data always contain noise. Therefore, it will affect the accuracy of modeling. Compare to type-1 fuzzy sets, the membership functions in type-2 fuzzy sets include primary membership function and secondary membership function. It provides additional degrees of freedom that make it possible to model uncertainties brought by the noise. In this paper, a type-2 T-S fuzzy model is presented to minimize the effect of measurement noise. Furthermore, the influence of the initial conditions is considered in the algorithm. The primary membership function is gained through an improved nearest-neighborhood clustering algorithm, and the secondary membership function is determined through GMM based on the sufficient statistics. The orthogonal least-squared algorithm is used to identify the consequent of the fuzzy rules. Finally, the simulation results are compared with those obtained from a type-1 T-S fuzzy modeling results and the superiority of the proposed approach is highlighted.