Construction of hierarchical fuzzy relational models from input-output data

As an important branch of fuzzy systems, hierarchical fuzzy systems (HFSs) are widely used in information science and engineering. Based on the semi-tensor product method, this paper investigates the hierarchical fuzzy relational models (HFRMs) of HFSs, and develops the corresponding construction algorithms. First, the construction methods of fuzzy relation matrices of fuzzy logic units (FLUs) are proposed by means of input-output data, based on which, the algebraic formulation is presented. After that, HFRMs of HFSs are explored via the fuzzy relation matrices based on the input-output data, and some effective algorithms are proposed to construct HFRMs with respect to the different hierarchical structures. Finally, the effectiveness of obtained results is verified by the on-ramp metering of freeway.