STRUCTURAL MODEL OF SIMILARITY FOR FUZZY CLUSTERING

As a generalization of the additive clustering model (Shepard, R. N. and Arabie, P. (1979)), we discuss the following three additive fuzzy clustering models: a simple additive fuzzy clustering model, an overlapping fuzzy clustering model and a fuzzy clustering model for ordinal scaled similarity. The essential merits of fuzzy clustering models are 1) the amounts of computations for the identification of the models are much fewer than a hard clustering model and 2) a fewer number of clusters is needed to get a suitable fitness. These fuzzy clustering models are extended to the model for asymmetric similarity. In this model, the concept of the similarity among clusters is introduced. The crucial assumption of this model is that the asymmetry of the similarity between the pair of objects is caused by the asymmetric similarity among clusters. The validity of this model is shown by some examples.