General fuzzy clustering model and neural networks

Abstract

This paper defines a generalized structural model of similarity between a pair of objects. We have discussed an additive fuzzy clustering model previously. The merits of the additive fuzzy clustering models are (1) the amount of computations for the identification of the models are much fewer than in a hard clustering model and (2) we obtain a suitable fitness by using fewer number of clusters. This paper proposes a general class of the clustering model, in which aggregation operators are used to define the degree of simultaneous belongingness of a pair of objects to a cluster. We discuss some required conditions for the aggregation operators. T-norms are concrete examples for satisfying these conditions. Moreover, the validity of this model is shown by investigating a characteristic of the model and numerical applications.<>