Learning the optimal parameter of the Hamacher t-norm applied for fuzzy-rule-based model extraction

Mamdani-type inference systems with trapezoidal-shaped fuzzy membership functions play a crucial role in a wide variety of engineering systems, including real-time control, transportation and logistics, network management, etc. The automatic identification or construction of such fuzzy systems input output data is one of the key problems in modeling. In the past years, the authors have investigated several different fuzzy t-norms, among others, algebraic and trigonometric ones, and the Hamacher product by substituting the standard “min” t-norm operation, in order to achieve better model fitting. In the present paper, the focus is on examining the general parametric Hamacher t-norm, where the free parameter quite essentially influences the quality of modeling and the learning capability of the model identification system. Based on a wide scope of simulation experiments, a quasi-optimal interval for the value of the Hamacher operator is proposed.