Ridders algorithm in approximate inversion of fuzzy model with parametrized consequences

Fuzzy models are known for their ability of precise data approximation. They can be used in automatic control as controllers. One of the techniques is based on inversion of fuzzy models. Fuzzy models can be inverted exactly or approximately. The exact inversion requires special features of fuzzy models. The approximate methods can be applied to a wider class of fuzzy models. The paper presents an approximate inversion of a fuzzy model with parametrized consequences. This fuzzy model cannot be inverted exactly. The presented approach inverts an existing fuzzy model with respect to any input. The inversion procedure uses the Ridders algorithm. The inversion is fast and does not require a separate training for each inverse input. The convergence of this approach is faster than linear. The paper formulates a theorem that shortens a search interval and may help to accelerate an inversion. The paper is accompanied by numerical examples.