A robust fuzzy clustering model for fuzzy data based on an adaptive weighted L1 norm

The imprecision related to measurements can be managed in terms of fuzzy features, which are characterized by two components: center and spread. Outliers affect the outcome of the clustering models. In trying to overcome this problem, this paper proposes a fuzzy clustering model for L-R fuzzy data, which is based on a dissimilarity measure between each pair of fuzzy data defined as an adaptive weighted sum of the L1-norms of the centers and the spreads. The proposed method is robust based on the metric and weighting approaches. It estimates the weight of a given fuzzy feature on a given fuzzy cluster by considering the relevance of that feature to the cluster; if outlier fuzzy features are present in the dataset, it tends to assign them weights close to 0. To deeply investigate the capability of our model, i.e., alleviating undesirable effects of outlier fuzzy data, we provide a wide simulation study. We consider the ability to classify correctly and the ability to recover the true prototypes, both in the presence of outliers. The comparison made with other existing robust methods indicates that the proposed methodology is more robust to the presence of outliers than other methods. Moreover, the performance of our method decreases more slowly than others when the percentage of outliers increases. An application of the suggested method to a real-world categorical dataset is also provided.