Quantile fuzzy regression based on fuzzy outputs and fuzzy parameters

A new approach is investigated to the problem of quantile regression modeling based on the fuzzy response variable and the fuzzy parameters. In this approach, we first introduce a loss function between fuzzy numbers which it can present some quantiles of fuzzy data. Then, we fit a quantile regression model between the available data based on proposed loss function. To evaluate the goodness of fit of the optimal quantile fuzzy regression models, we introduce two indices. Inside, we study the application of the proposed approach in modeling some soil characteristics, based on a real data set.