20.4 Prediction in fuzzy regression models
Depending on the assumed regression model, predictions of dependent values for values of the independent variable where no data are given can be obtained using the generalized algebraic operations for fuzzy quantities.
The predictions depend on the different cases (a)–(e) given at the start of the chapter.
ad (a): In this case the estimated parameters are fuzzy numbers j* and the predicted value Therefore y*(x) is a fuzzy number whose characterizing function is obtained by the generalized arithmetic operations.
ad (b): For the prediction the situation is essentially the same as in (a).
ad (c): By the estimation procedure for θj the estimators are fuzzy values j*, and the prediction equation reads
Therefore fuzzy multiplication as well as fuzzy addition has to be applied here.
ad (d): Here the prediction equation based on observed data is the same as in case (c).
ad (e): Again the prediction equation has the form from case (c).
For applications triangular fuzzy numbers are not sufficient. Frequently trapezoidal fuzzy numbers are ...