Fuzzy least absolute linear regression

The distance between triangular fuzzy numbers is an important research topic in many fields. In this paper, we introduce a new distance between triangular fuzzy numbers, merge least absolute deviation method with the new distance and propose fuzzy regression model. We also investigate the properties and model algorithm of fuzzy least absolute linear regression model in detail by transforming this model into linear programming. Further, we use three numerical examples to illustrate our proposed model reasonable and make some comparisons with some existing fuzzy regression models. Finally, we investigate the robust property of our proposed model and apply our model in the missing data set to verify model data.