Modeling Hydrology Data Using a Robust Least Trimmed Squares Fuzzy Regression Approach

Document Type : Original Paper


1 Department of Statistics, Semnan University, Semnan, Iran

2 Semnan University


Estimation methods of parameters of fuzzy least-squares regression have very sensitivity to unusual data (e.g. outliers). In the presence of outliers, most of the existing estimation methods of parameters of this kind of models using least-squares approach provide unexpected and unreliable estimators with amounts of errors. Therefore, in this paper a robust least trimmed squares fuzzy regression model is described for modeling for crisp input-fuzzy output variables. In this approach, the constructed target function in model parameter estimation problem in such a way which minimizes the sum of the  smallest squared residuals. This method has an algorithm that estimates the optimal values of the parameters based on different selected combinations of  good observations of the data set of size . Therefore, this method has the ability of reducing the effects of such a data in estimation of the parameters of the model. Finally, the investigated fuzzy regression model is applied and studied to modeling real-world data set in hydrology which sometimes contains outlier points. In this regard, a comparison study between the proposed method and ordinary least squares fuzzy regression method is considered. The comparison results of the applied study reveal that for this particular data set the proposed method performs better fitting than the well-known ordinary fuzzy least-squares regression model. Also the proposed method identified the points that have bad effect on estimation problem of the parameters.


Main Subjects

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