Fuzzy double-ordered c-regression models based on fuzzy S-estimators

Among the most popular clustering methods is the fuzzy c-means one. Its generalization by application of hyperplane shaped prototypes of the clusters is known as the Fuzzy C-Regression Models (FCRM) method. Since this method is very sensitive to poor initialization and to the presence of noise and outliers in data, its numerous robust variants have been introduced, using also the ordering operation. In this paper, a new variation of the method has been introduced which uses ordering for the residuals of each model and ordering for residuals of each data pair, and additionally, uses a fuzzy S-regression estimator associated with M-scale to improve significantly the method robustness. Thus, the concept of a fuzzy S-regression estimator is also introduced. The new method is named as the Fuzzy Double Ordered C-Regression Models (FDOCRM) method. The method proposed is compared to a few other important reference ones. Large-scale simulations demonstrate its competitiveness and usefulness.