Fuzzy clustering of fuzzy data based on robust loss functions and ordered weighted averaging

In many real cases the data are not expressed in term of single values but are imprecise. In all these cases, standard clustering methods for single-valued data are unable to properly take into account the imprecise nature of the data. In this paper, by considering the Partitioning Around Medoids (PAM) approach in a fuzzy framework, we propose a fuzzy clustering method for imprecise data formalized in a fuzzy manner. In particular, in order to neutralize the negative effects of possible outlier fuzzy data in the clustering process, we proposed a robust fuzzy c-medoids clustering method for fuzzy data based on the combination of Huber's M-estimators and Yager's OWA (Ordered Weighted Averaging) operators. The proposed method is able to smooth the influence of anomalous data by means of a suitable parameter, the so-called typicality parameter, capable to tune the influence of the outliers. The performance of the proposed method has been shown by means of a simulation study, composed of experiments on: (i) simple two-dimensional dataset, (ii) benchmark datasets and (iii) the fuzzy-art-outliers dataset. The comparison made with the robust clustering methods known from the literature indicates the competitiveness of the introduced method to others. An application of the suggested method to a real dataset is also provided and the results of the method has been compared with other clustering methods suggested in the literature. In the application, the comparative assessment has shown the informational gain (in term of additional information) of the proposed method vs the other robust methods.