Abstract
Multi-input multi-output (MIMO) hierarchical fuzzy systems (HFSs) play a significant role in industrial process control and power systems. Using the max-min semi-tensor product of matrices, this paper proposes the algebraic formulation of MIMO HFSs, and discusses the corresponding interpretability. Firstly, the parallel fuzzy relation matrix (FRM) of MIMO fuzzy systems is proposed, based on which, an algebraic formulation of MIMO fuzzy systems is developed. Secondly, the factorization of parallel FRM is used to partition the MIMO fuzzy systems into fuzzy logic units (FLUs). Based on this operation, the algebraic formulations and construction algorithms of serial, parallel and hybrid MIMO HFSs are established. Thirdly, the algebraic formulations are used to study the universal approximation and interpretability of MIMO HFSs, and the optimal interpretability is obtained. Finally, the effectiveness of the obtained results is verified by the energy control systems in parallel hybrid vehicles.
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