Some results on a multivariate generalization of the fuzzy least square regression

Fuzzy regression techniques can be used to fit fuzzy data into a regression model, where the deviations between the dependent variable and the model are connected with the uncertain nature either of the variables or of their coefficients. P.M. Diamond (1988) treated the case of a simple fuzzy regression of an uncertain dependent variable on a single uncertain independent variable, introducing a metrics into the space of triangular fuzzy numbers. In this work we managed more than a single independent variable, determining the corresponding estimates and providing some theoretical results about the decomposition of the sum of squares of the dependent variable according to Diamond's metric, in order to identify its components.