In fuzzy regression, that was first proposed by Tanaka et al. (Eur J Oper Res 40:389-396, 1989; Int Cong Appl Syst Cybern 4:2933-2938, 1980 IEEE Trans Syst Man Cybern 12:903-907, 1982), there is a tendency that the greater the values of independent variables, the wider the width of the estimated dependent variables. This causes a decrease in the accuracy of the fuzzy regression model constructed by the least squares method.This paper suggests the least absolute deviation estimators to construct the fuzzy regression model, and investigates the performance of the fuzzy regression models with respect to a certain error measure. Simulation studies and examples show that the proposed model produces less error than the fuzzy regression model studied by many authors that use the least squares method when the data contains fuzzy outliers.

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This article introduces a general fuzzy regression model, which separates the response function on a mode and spreads of an -level set for an observed fuzzy number, to estimate a fuzzy relation between two fuzzy random variables. We construct the general fuzzy regression model using least squares estimation and best response functions on the mode and spread of an -level set for the fuzzy number when the response variable is an LR-fuzzy number and independent variables are crisp numbers. Then we derive a crisp mean and variance of the predicted fuzzy number, and compare the accuracy of our proposed fuzzy regression model with other fuzzy regression models suggested by many authors.

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