OWA operators in regression problems

We consider an application of fuzzy logic connectives to statistical regression. We replace the standard least squares, least absolute deviation, and maximum likelihood criteria with an ordered weighted averaging (OWA) function of the residuals. Depending on the choice of the weights, we obtain the standard regression problems, high-breakdown robust methods (least median, least trimmed squares, and trimmed likelihood methods), as well as new formulations. We present various approaches to numerical solution of such regression problems. OWA-based regression is particularly useful in the presence of outliers, and we illustrate the performance of the new methods on several instances of linear regression problems with multiple outliers.