A fuzzy empirical quantile-based regression model based on triangular fuzzy numbers

Quantile regression estimates conditional quantiles and has found extensive applications in real-life statistical procedures. This study assessed a new for nonlinear quantile regression modeling in cases where response variables are reported by triangular fuzzy numbers and predictors are exact data. For this purpose, the notion of the conditional quantile of a fuzzy random variable giving exact values and its empirical estimation were introduced. Then, a fuzzy empirical kernel-based quantile regression method was developed using a hybrid algorithm to evaluate the unknown bandwidth and quantile level. For this purpose, a sign distance measure was introduced for triangular fuzzy numbers. The proposed sign distance measure was also compared with a well-known sign distance frequently used in fuzzy environments. The proposed method was also compared with other fuzzy regular quantile regression models as well as some common fuzzy linear/nonlinear regression models in terms of popular goodness-of-fit measures. A simulation study was also conducted to evaluate the performance of the proposed method. Two applied examples were investigated using the proposed method, as well. Simulations and the applied examples indicated the better fit of the proposed fuzzy empirical quantile regression model with the data set as compared with the existing fuzzy quantile regression models and other fuzzy regression methods.