A new fuzzy regression model based on least absolute deviation.

Fuzzy set theory is a powerful tool to describe and process uncertainty information which exist in real world, and fuzzy regression is an important research topic which can be used to fulfill predicting by establishing the functional relationship between fuzzy variables. Trapezoidal fuzzy number is a common one which can represent other types of fuzzy numbers, and least absolute deviation is a robust method which is insensitive to outliers. So, in this paper, we propose a new fuzzy regression model based on trapezoidal fuzzy number and least absolute deviation method. Firstly, we introduce a new distance measure between trapezoidal fuzzy numbers which is the basis for applications, and merge least absolute deviation with the proposed distance measure to investigate fuzzy regression model whose parameters can be trapezoidal fuzzy numbers. Meanwhile, we investigate the model algorithms for three cases in detail, including different types of inputs, outputs and regression coefficients. Finally, we use four numerical examples to illustrate that our proposed model is reasonable, compare our proposed model with some existing fuzzy regression models, and do comprehensive analysis about the proposed model. The results show that our proposed model is robust, and has better fitting effect.