Least-squares approach to regression modeling in full interval-valued fuzzy environment

A regression procedure is introduced when the observations of the response and the independent variables, as well as the coefficients that are to be estimated, are triangular interval-valued fuzzy numbers (IVFNs). The coefficients of the model are obtained by least square method, using a distance that we define on the space of IVFNs. Three real data sets, on soil sciences and hydrology engineering are used to test the applicability of the proposed method. The predictive performance of the models thus obtained are examined by cross-validation. To check the overall performance of the proposed method, two measures of goodness of fit are introduced and employed.