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This work focuses on robust clustering of data affected by imprecision. The imprecision is managed in terms of fuzzy sets. The clustering process is based on the fuzzy and possibilistic approaches. In both approaches the observations are assigned to the clusters by means of membership degrees. In fuzzy clustering the membership degrees express the degrees of sharing of the observations to the clusters. In contrast, in possibilistic clustering the membership degrees are degrees of typicality. These two sources of information are complementary because the former helps to discover the best fuzzy partition of the observations while the latter reflects how well the observations are described by the centroids and, therefore, is helpful to identify outliers. First, a fully possibilistic k -means clustering procedure is suggested. Then, in order to exploit the benefits of both the approaches, a joint possibilistic and fuzzy clustering method for fuzzy data is proposed. A selection procedure for choosing the parameters of the new clustering method is introduced. The effectiveness of the proposal is investigated by means of simulated and real-life data. [ABSTRACT FROM AUTHOR]

Abstract: In possibilistic clustering objects are assigned to clusters according to the so-called membership degrees taking values in the unit interval. Differently from fuzzy clustering, it is not required that the sum of the membership degrees of an object to all clusters is equal to one. This is very helpful in the presence of outliers, which are usually assigned to the clusters with membership degrees close to zero. Unfortunately, a drawback of the possibilistic approach is the tendency to produce coincident clusters. A remedy is to add a repulsion term among prototypes in the loss function forcing the prototypes to be far ‘enough’ from each other. Here, a possibilistic clustering algorithm with repulsion constraints for imprecise data, managed in terms of fuzzy sets, is introduced. Applications to synthetic and real fuzzy data are considered in order to analyze how the proposed clustering algorithm works in practice. [Copyright &y& Elsevier]