Fuzzy regression model with interval-valued fuzzy input-output data

A novel approach is introduced to construct a fuzzy regression model when both input data and output data are interval-valued fuzzy numbers. Using a distance on the space of interval-valued fuzzy numbers, a least-squares method is developed. Also, a nonlinear programming model is proposed to estimate the crisp parameters for the interval-valued fuzzy regression model. A real example demonstrates the feasibility and efficiency of the proposed method. Moreover, two goodness of fit indices are introduced and employed for more evaluation of such fuzzy interval-valued regression models.