Fuzzy Gradient Boosting Machine Framework Using Different Fuzzy Distances

Gradient Boosting Machine (GBM) models are widely used in regression and classification problems and can give effective results. These models are models that use simple basic learners iteratively by weighting them repeatedly. Most of the time, decision stumps are used as the basic learners. In the operation of the algorithm, it is necessary to calculate the derivative of the residuals and loss function. In this study, theoretical investigations have been made to calculate residuals, derivatives and loss functions when the target values ​​are fuzzy numbers. In the case of using triangular fuzzy numbers, definitions are given and theorems are proved in order to alleviate the computational load. Fuzzy SSE-GBDR and Fuzzy LAD-GBDR algorithms are proposed in accordance with the use of quadratic and absolute loss functions, and the base learner in the form of decision stamp. Calculation experiments were made on Diabetes and Car Prices datasets, which are used in the literature. As a result of the calculations, it has been shown that the proposed new algorithms give accurate results