System identification of fuzzy relation matrix models by semi-tensor product operations

In order to facilitate the representation of fuzzy relation matrix (FRM) models, a new system identification technique is proposed in this work to recognize the architecture and parameters of FRM models based on the semi-tensor product (STP) operation. Firstly, a fuzzy STP algorithm is defined for fuzzy inference. Secondly, a novel FRM framework is proposed for system parameter identification. Thirdly, the recognized FRM parameters are optimized to improve fuzzy system performance by the use of a hybrid training method based on the least squares estimator and the recursive Levenberg-Marquaedt algorithm. The effectiveness of the proposed structure and parameter identification techniques is verified by simulation of a multi-steps-ahead prediction modeling. Simulation results show that the proposed fuzzy STP technology is efficient for system identification, and the proposed matrix expression can be used to design multi-input multi-output (MIMO) systems with fuzzy FRM models.