Experimental Assessment of Heterogeneous Fuzzy Regression Trees

José Luis Corcuera Bárcena, Pietro Ducange, Riccardo Gallo, Francesco Marcelloni, Alessandro Renda, Fabrizio Ruffini

Abstract: Fuzzy Regression Trees (FRTs) are widely acknowledged as highly interpretable ML models, capable of dealing with noise and/or uncertainty thanks to the adoption of fuzziness. The accuracy of FRTs, however, strongly depends on the polynomial function adopted in the leaf nodes. Indeed, their modelling capability increases with the order of the polynomial, even if at the cost of greater complexity and reduced interpretability. In this paper we introduce the concept of Heterogeneous FRT: the order of the polynomial function is selected on each leaf node and can lead either to a zero-order or a first-order approximation. In our experimental assessment, the percentage of the two approximation orders is varied to cover the whole spectrum from pure zero-order to pure first-order FRTs, thus allowing an in-depth analysis of the trade-off between accuracy and interpretability. We present and discuss the results in terms of accuracy and interpretability obtained by the corresponding FRTs on nine