A proposal of robust regression for random fuzzy sets

Abstract

In standard regression the Least Squares approach may fail to give valid estimates due to the presence of anomalous observations violating the method assumptions. A solution to this problem consists in considering robust variants of the parameter estimates, such as M-, S- and MM-estimators. In this paper, we deal with robustness in the field of regression analysis for imprecise information managed in terms of fuzzy sets. Although several proposals for regression analysis of fuzzy sets can be found in the literature, limited attention has been paid to the management of possible outliers in order to avoid inadequate results. After discussing the concept of outliers for fuzzy sets, a robust regression method is introduced on the basis of one of the proposals available in the literature. The robust regression method is applied to a synthetic data set and a comparison with the non-robust counterpart is given. © 2013 Springer-Verlag.