An OWA-based approach to quantile fuzzy regression

In this article, a new approach is introduced to estimate the parameters of the quantile fuzzy regression model with mathematical programming based on the weighted aggregation of ordered errors/deviations/residuals. With regard to the proper determination of the operator weights appeared in the optimization problem, Ordered Weighted Averaging (OWA) operators provide important tools for exploring the dataset of the fuzzy regression relationship and providing the entire description of the individuals as good or bad (outlier) data points. It is proven that this method is useful in practice due to its robustness against outliers as well as flexibility in dealing with unusual observations. Moreover, an algorithm is deduced for the estimation method and the proper selection of the tuning parameter which labels the outlier points. Except for the parameter estimation and outlier selection of the proposed method, this research focuses on the application of the proposed method on both simulation studies and real example.