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.

为了便于表示模糊关系矩阵（FRM）模型，在这项工作中提出了一种新的系统识别技术，以识别基于半张量积（STP）运算的 FRM 模型的体系结构和参数。首先，定义了模糊推理的模糊STP算法。其次，提出了一种新的 FRM 框架用于系统参数识别。第三，通过使用基于最小二乘估计器和递归 Levenberg-Marquaedt 算法的混合训练方法，优化识别的 FRM 参数以提高模糊系统性能。所提出的结构和参数识别技术的有效性通过多步提前预测建模的模拟得到验证。