A Generalized Fuzzy Clustering Model Based on Aggregation Operators and its Applications

Abstract

This paper proposes a fuzzy clustering model which defines a generalized structural model of similarity between a pair of objects.The structure of an observed similarity is usually unknown and complicated, and so various fuzzy clustering models are required to identify the latent structure of the similarity data. Therefore, we define the general class of fuzzy clustering models, so as to represent many different structures of a similarity data. In order to define the generalized fuzzy clustering model, we use aggregation operators for representing the degree of simultaneous belongingness of a pair of objects to a cluster, and define some required conditions for the operators. T-norms are examples to satisfy these conditions.Moreover, asymmetric aggregation operators are proposed to apply asymmetric similarity data. The asymmetric operators are defined by using generator function of T-norms. The validity of this model is shown by investigating the characteristic feature of the model and numerical applications.