Nonlinear autoregressive model based on fuzzy relation

A nonlinear autoregressive model that has a regressive function approximated by fuzzy relations is proposed. The internal parameters of the fuzzy relational matrix describe the characteristics of this function. The estimation method of these parameters is shown from the viewpoint of maximum likelihood estimation. As a result of the numerical experiment on artificial data compared with the ordinary autoregressive model and the polynomial autoregressive model, it is shown that the proposed model is able to estimate the more precise regressive function from the observed data.