An enhanced fuzzy linear regression model with more flexible spreads

One of the deficiencies of previous fuzzy linear regression models is that with the increase of the magnitudes of independent variables, the spreads of estimated fuzzy dependent variables are increasing, even though the spreads of observed dependent variables actually decrease or remain unchanged. Some solutions have been proposed to solve this spreads increasing problem. However, those solutions still cannot model a decreasing trend in the spreads of the observed dependent variables as the magnitudes of the independent variables increase. In this paper we propose an enhanced fuzzy linear regression model (model FLR_FS), in which the spreads of the estimated dependent variables are able to fit the spreads of the observed dependent variables, no matter the spreads of the observed dependent variables are increased, decreased or unchanged as the magnitudes and spreads of the independent variables change. Four numerical examples are used to demonstrate the effectiveness of model FLR_FS.