OWA fuzzy regression

Abstract

In this paper, the Ordered Weighted Averaging (OWA) operators will be considered to propose general fuzzy regression modeling technique for crisp/fuzzy-input fuzzy-output data. Here, by considering various kinds of a special form of OWA operators we will be able to1.investigate different approaches for aggregation of residuals/errors,2.construct a multi-objective optimization problem,3.provide high-breakdown estimators,4.identify poorly fitted data points, which might be considered as outliers while limiting their effects on the model,5.show how robust alternatives to other fuzzy regression models can be obtained as a result. Finally, a special case of the OWA-based fuzzy regression model known as OWA-Least Trimmed Absolutes Deviations (OWA-LTAD) fuzzy regression model is studied in details for crisp-input fuzzy-output data. An algorithm is investigated in the present study for estimation process in which1.the highest breakdown value will always be achieved (up to the maximum of 0.5) for problems with multiple outliers,2.the poorly fitted dataset can be labeled as outliers in an elemental set. In the presence of multiple outliers, the new method is particularly useful, and the performance of the proposed approach is illustrated for modeling several simulated datasets and a real valued dataset all contaminated with multiple outliers as well. We will look at an application of the proposed approach, in particular, to detect outliers in such models.