Fuzzy robust regression analysis based on a hyperelliptic function

Since a fuzzy linear regression model was proposed in 1987, its possibilistic model is employed to analyze data in various fields. From view points of fuzzy linear regression, data are interpreted to express the possibilities of a latent system. Therefore, when data have error or samples are irregular, the obtained regression model has unnaturally too wide possibility range. In this paper we propose a fuzzy robust linear regression model which is not influenced by data with error. Especially a hyperelliptic function is employed to select focal samples which may have large error or be irregular so that the number of combinatorial calculations can be reduced to a great extent. The model is built to minimize the total error between the model and the data. The robustness of the model is shown using numerical examples.