Abstract
In the existing regression model for the fuzzy linear function, fuzzy parameters are derived by solving a linear programming problem so that the fuzzy dependent variable or fuzzy output contains the estimated fuzzy output with more than a certain predetermined degree while the total fuzziness of the estimated outputs becomes minimal in the so-called minimization formulation. It is easily shown that the above mentioned formulation of the problem falls through when the width of the output shrinks away, in other words, the output data is non-fuzzy. Thus, it is clear that the existing model does not include the non-fuzzy linear regression model as its extreme case. In this study proposed is a new fuzzy linear regression model based on the minimization criterion of the sum of squared distance(Euclidean distance over the center and width space) between the observed fuzzy output and its estimate The model is reduced to the usual non-fuzzy regression model when the width of the output variable vanishes. Numerical test results demonstrate that the proposed model substantially outperforms the existing model in both estimating output center and output width.
