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On A General Fuzzy Additive Clustering Model

ABSTRACTThe purpose of this article is to define a generalized structural model of similarity between a pair of objects. Applying a classification of a given data set as a structural model, we have developed an additive fuzzy clustering model.7,8 The essential merits of the additive fuzzy clustering models are 1) the amount of computations for the identification of the models are much fewer than a hard clustering model and 2) fewer number of clusters are needed to get a suitable fitness.9 This article proposes a general class of the clustering model, in which fuzzy aggregation operators are used to define a degree of simultaneous belongingness of a pair of objects to a cluster. We discuss some required conditions for the fuzzy aggregation operators. T-norm is a concrete example to satisfy the conditions. Moreover, the validity of this model is shown by investigating the characteristic feature of the model and numerical applications.