An explainable fused lasso regression model for handling high-dimensional fuzzy data

In machine learning, the fused lasso is a regularization technique that is used to handle problems where the underlying signal has some kind of structure. In this paper, we extend fused lasso estimation for regression models characterized by fuzzy predictors and fuzzy responses. We present the first fused lasso regression model that is able to handle and analyze high-dimensional fuzzy data. The proposed model provides feature selection, leads to an improved predictive performance, and ensures interpretable and explainable models, all while being computationally efficient. Moreover, it can recover the true signal more accurately, find solutions that are structurally sparse, and is robust to noise. We conduct comprehensive comparative analysis and demonstrate the practical applicability of the presented fuzzy regression model through simulation and real-life applications.