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 quantifies different types of uncertainties, such as nonspecificity, conflict, 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 simplification method, based on similarity between fuzzy sets and significance of these sets. The proposed model can provide predictions in several different 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.