This paper introduces a recursive relation between an existing Takagi–Sugeno–Kang (TSK) fuzzy system of order   $n$   and systems of order    $n-1$   and   $0$   . The presented method helps to realize higher order TSK fuzzy systems using first- and zero-order TSK fuzzy system models, which are available in simulation software (e.g., MATLAB and its toolboxes). This method has two major benefits: 1) easier and faster simulation of higher order TSK systems using available software; and 2) possibility of tuning high-order TSK systems by methods like ANFIS, which can only tune first- and zero-order TSK systems. The final section of this paper includes a comparison of simulation speed if the proposed method is used or not and nonlinear function estimation by applying ANFIS on high-order TSK system using the proposed method. Simulation results prove the superiority and usefulness of the proposed method.
['Gholamali Heydari', 'Ali Akbar Gharaveisi', 'MohammadAli Vali']
New Formulation for Representing Higher Order TSK Fuzzy Systems