Fuzzy regression analysis based on M-estimates

The least-squares technique has been shown to possess valuable properties as a method of the parameter estimation of classic and fuzzy regression analysis. However, the behavior and properties of the least-squares estimators are affected when outliers arise in the sample and/or by slight changes in the dataset. Robust techniques, on the other hand, provide robust estimators of the parameters which avoid such adverse effects. For this purpose, this paper extends the M-estimation approach to fuzzy regression analysis which provides consistent results in the presence of outliers. The parameters estimation problem is reduced to a reweighted algorithm which is a simple approach both theoretically and computationally. The proposed algorithm decreases the effect of outliers on the model fit by down-weighting them. To show the performances of the proposed method against some commonly used fuzzy regression models simulation studies, and two applicative examples based on real-world datasets in hydrology and atmospheric environment are provided. The sensitivity analysis of the estimated parameters are also reported based on a Monte-Carlo simulation study showing the efficiency of the proposed estimators in comparison with some other well-known methods in fuzzy regression analysis.