A General Fuzzy Clustering Model Based on Aggregation Operators

Abstract

The purpose of this paper is to propose a generalized clustering model. The structure of an observed similarity is usually unknown and complicated, so various fuzzy clustering models are required to identily the latent structure of the similarity data. Therefore, we define a general class of fuzzy clustering models, so as to represent many different structures of a similarity data. We have been discussed the additive fuzzy clustering model (Sato and Sato, 1994a, 1994b). The merits of the 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 a using fewer number of clusters (Sato and Sato, 1994c). In the generalized clustering model, aggregation operators are used to define the degree of simultaneous belongingness of a pair of objects to a cluster. We will 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 its numerical applications.