A new fuzzy formulation technique based on semitensor product of matrices is proposed in this paper to construct multivariable fuzzy logic systems. A fuzzy relation matrix (FRM) model is suggested for direct modeling and indirect identification of the fuzzy matrix expression using the observed input-output data of fuzzy dynamical process. The center points of fuzzy sets for every output variable are optimized by using least squares estimation. The effectiveness of the proposed fuzzy formulation technology is verified by simulations. Test results show that the proposed formulation technique is an effective design method to construct and optimize fuzzy relation structure matrices for multivariable fuzzy systems. It can be used to design FRM models for multi-input multi-output systems.

中文翻译：

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用半张量积建模多变量模糊系统


本文提出了一种基于矩阵半张量积的模糊表述技术来构造多变量模糊逻辑系统。建议使用模糊关系矩阵（FRM）模型，使用观测到的模糊动态过程的输入输出数据来直接建模和间接识别模糊矩阵表达式。通过使用最小二乘估计来优化每个输出变量的模糊集的中心点。通过仿真验证了所提出的模糊表述技术的有效性。测试结果表明，所提出的公式化技术是构造和优化多变量模糊系统模糊关系结构矩阵的有效设计方法。它可用于设计多输入多输出系统的FRM模型。