Fuzzy regression analysis is an extension of the classical regression analysis that is used in evaluating the functional relationship between the dependent and independent variables in a fuzzy environment. Fuzzy regression has been criticized because it is sensitive to outliers, it does not allow all data points to influence the estimated parameters, and the spread of the estimated values become wider as more data are included in the model. In this paper, we consider the problem of deleting bad influential observations (outliers) in fuzzy linear regression models. We develop a fuzzy least-square regression model with importing penalty costs for discarding outliers that are inserted into the loss function. The robust procedure is formulated as a Quadratic Mixed Integer Programming (QMIP) problem.
