Handling Different Forms of Uncertainty in Regression Analysis: A Fuzzy Belief Structure Approach

We propose a new approach to functional regression based on fuzzy evidence theory. This method uses a training set for computing a fuzzy belief structure which quantiies diierent types of uncertainties, such as nonspeciicity, connict, or low density of input data. The method can cope with a very large class of training data, such as numbers, intervals , fuzzy numbers, and, more generally, fuzzy belief structures. In order to limit calculations and improve output readability, we propose a belief structure simpliication method, based on similarity between fuzzy sets and signiicance of these sets. The proposed model can provide predictions in several diierent forms, such as numerical, probabilistic, fuzzy or as a fuzzy belief structure. To validate the model, we propose two simulations and compare the results with classical or fuzzy regression methods.