Fuzzy and possibilistic clustering for fuzzy data

The Fuzzy kk-Means clustering model (FkkM) is a powerful tool for classifying objects into a set of kk homogeneous clusters by means of the membership degrees of an object in a cluster. In FkkM, for each object, the sum of the membership degrees in the clusters must be equal to one. Such a constraint may cause meaningless results, especially when noise is present. To avoid this drawback, it is possible to relax the constraint, leading to the so-called Possibilistic kk-Means clustering model (PkkM). In particular, attention is paid to the case in which the empirical information is affected by imprecision or vagueness. This is handled by means of LR   fuzzy numbers. An FkkM model for LR   fuzzy data is firstly developed and a PkkM model for the same type of data is then proposed. The results of a simulation experiment and of two applications to real world fuzzy data confirm the validity of both models, while providing indications as to some advantages connected with the use of the possibilistic approach.