WABL method as a universal defuzzifier in the fuzzy gradient boosting regression model

Abstract

Gradient Boosting Regression (GBR) models are widely used and can give effective results in regression and classification problems. The main value of the approach proposed in this study is that it allows the GBR algorithm to be used even if the target variables are fuzzy. The defuzzification strategy affects the solutions found. The solutions of the GBR algorithm, depending on various defuzzification strategies, in case the target values are fuzzy numbers, are examined. Techniques have been proposed for calculating fuzzy residuals and loss functions. Definitions and theorems are given to alleviate the computational load on triangular fuzzy numbers. Results of the Fuzzy GBR algorithm were compared on ten popular datasets using COG (Center of Gravity), MOM (Mean of Maxima) and WABL (Weighted Averaging Based on Levels) defuzzification methods. The fuzzy R-squared and the fuzzy RMSE (Root Mean Square Error) scores defined on the basis of fuzzy distance was used to evaluate the results obtained via different defuzzification methods. It has been seen that if the parameters of the WABL method are adjusted appropriately, it gives better results than other defuzzification methods in all data sets, so the WABL can be handled as a universal defuzzifier in the Fuzzy GBR models.