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Universal Approximation of Fuzzy Relation Models by Semitensor Product

A universal approximation of multi-input multi-output (MIMO) fuzzy systems is proposed in this article based on a fuzzy relation matrix (FRM) method. The fuzzy reasoning operation in FRM is realized by the semitensor product (STP) technique. The theoretical proof is provided to estimate approximation accuracy of the FRM models for MIMO systems. Its effectiveness is verified by simulation. Simulation results show that the proposed fuzzy design technology is efficient for fuzzy systems modeling, and the general universal approximation theory can be extended to the MIMO fuzzy systems. The proposed uniform matrix expression can be used to design fuzzy systems with FRM models and to approximate nonlinear functions with required accuracy.