Abstarct: If the regularity assumptions of least squares method are satisfied, the estimates of this method willbe known as the best one. If outliers exist in a data set, traditional methods won’t result in good consequences and we should use the alternative robust regression. On the other hand, when we have fuzzy observations, we can’t use the traditional ethods to model them. So we should use the alternative fuzzy regression. When we have both fuzzy observations and outliers in a data set, we should use the alternative fuzzy robust regression. After introducing the possibilistic fuzzy linear regression, fuzzy regression analysis has been widely studied and applied in various areas. Also, the least square methods were genelalized in fuzzy environment. These methods are sensitive to the present of outliers. In this dissertation, two fuzzy regression analyses are proposed. When independent variables are crisp, the dependent variable is a fuzzy number and outliers exist in data set. The first method is a modified fuzzy least squares regression analysis and the second method is a modified fuzzy absolute deviations regression analysis. Results demonstrate that the second method is better than the first.In these two methods, the residuals are ranked and then the weight matrices are constructed by defiened membership functions. Fuzzy least squares estimations and fuzzy least absolute deviations are obtained by these weight matrices.