Generalized operators and its application to a nonlinear fuzzy clustering model

In this paper, a generalized operator based nonlinear fuzzy clustering model is proposed. Target data of this model is similarity data and the obtained similarity data has various structures. Therefore, for general-purpose, the generalized operators are defined on a product space of linear spaces in order to consider the variety of the structures of similarity between a pair of objects by revising the aggregation operators from the binary operator to a function on a product space. Ị umerical examples using artificial data and diagnostic breast cancer data show the potential utility of the general-purpose model and better performance when compared with an ordinary nonlinear fuzzy clustering model such as a kernel fuzzy clustering model.