A least square approach for the detection and removal of outliers for fuzzy linear regressions

Fuzzy linear analysis may lead to an incorrect interpretation of data in case of being incapable of dealing with outliers. Both basic probabilistic and least squares approaches are sensitive to outliers. In order to detect the outliers in data, we propose a two stage least squares approach which in contrast to the other proposed methods in the literature does not have any user defined variables. In the first stage of this approach, the outliers are detected and the clean dataset is prepared and then in the second stage a model is sought to fit the clean dataset. In both the first and second phases, the minimization of the model fitting measurement is achieved with hybrid optimization which gives us the flexibility of using any type of a model fitting measure regardless of being continuous or differentiable.