An Additive Fuzzy Clustering Model for Similarity on Ordinal Scale
by
Yoshiharu Sato
Hokkaido University, JAPAN
Coauthors: Hideyuki Imai (Hokkaido University), Mika Sato (University Tukuba)

A pioneering work to apply the concept of fuzzy sets to a cluster analysis was made by E.Ruspini(1969). Since the fuzzy k-means clustering algorithm was proposed by J.C.Dunn(1973) and J.C.Bezdek(1987), several methods of fuzzy clustering have developed rapidly and many applications have been suggested.

On the other hand, the additive clustering model (ADCLUS) in hard(non-fuzzy) cluster analysis has been proposed by R.N.Shepard and P.Arabie(1979). In this model, the clusters are defined as the groups whose elememts share the common properties.

By introducing the concept of the fuzzy cluster into the ADCLUS model, we can construct a natural fuzzy clustering model which is possible to interpret as the structure of similarity. The essential merits of the additive fuzzy clustering models are 1) the amount of computations for the identification of the model are much fewer than a hard ADCLUS model and 2) fewer number of clusters are needed to get a suitable fitness.

This paper proposes an additive fuzzy clustering model for ordinal similarity data, in which fuzzy aggregation operators are used to define a degree of simultaneous belongingness of a pair of objects to a cluster. The practical solution is given by an algorithm based on the monotone regression principle.

Date received: October 13, 2000