Extended fuzzy linear models and least squares estimates

Least squares regression of the fuzzy linear model is extended to overcome and interpret the occurrence of negative spreads [1]. The idea is to introduce best fit difference models which exploit both the Hukuhara difference and the L2-metric distance. The fuzzy models use LR-fuzzy numbers. Fitted models are compared by using the coefficient of determination, in a similar way to its use in classical statistical least squares fitting. The non-LR-fuzzy case is also considered.