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This paper describes two new online fuzzy clustering algorithms based on medoids. These algorithms have been developed to deal with either very large datasets that do not fit in main memory or data streams in which data are produced continuously. The innovative aspect of our approach is the combination of fuzzy methods, which are well adapted to outliers and overlapping clusters, with medoids and the introduction of a decay mechanism to adapt more effectively to changes over time in the data streams. The use of medoids instead of means allows to deal with non-numerical data (e.g. sequences...) and improves the interpretability of the cluster centers. Experiments conducted on artificial and real datasets show that our new algorithms are competitive with state-of-the-art clustering algorithms in terms of purity of the partition, F1 score and computation times. Finally, experiments conducted on artificial data streams show the benefit of our decay mechanism in the case of evolving distributions.