Nonparametric regression analysis of uncertain and imprecise data using belief functions Original Research Article

This paper introduces a new approach to regression analysis based on a fuzzy extension of belief function theory. For a given input vector x, the method provides a prediction regarding the value of the output variable y, in the form of a fuzzy belief assignment (FBA), defined as a collection of fuzzy sets of values with associated masses of belief. The output FBA is computed using a nonparametric, instance-based approach: training samples in the neighborhood of x are considered as sources of partial information on the response variable; the pieces of evidence are discounted as a function of their distance to x, and pooled using Dempster’s rule of combination. The method can cope with heterogeneous training data, including numbers, intervals, fuzzy numbers, and, more generally, fuzzy belief assignments, a convenient formalism for modeling unreliable and imprecise information provided by experts or multi-sensor systems. The performances of the method are compared to those of standard regression techniques using several simulated data sets.