Fuzzy clustering model for asymmetry and self-similarity

Abstract

This paper shows a method of classification for asymmetric similarity data and non-reflexive data. In a clustering problem in which the similarities of the objects are given by the relation like mobility data which shows relation of proximity from one object to another object, the ordinary fuzzy clustering models are not available. In this paper, these data are treated as asymmetric similarity data including non-reflexive elements which are defined by diagonal elements of the similarity matrix. We define asymmetric aggregation operators to classify objects based on asymmetric similarities. Using the asymmetric aggregation operators, clusters which represent the asymmetric structure between objects are obtained. Moreover, the estimated parameter is introduced to show the non-reflexive data. The validity of this model is shown both by investigating the features of the asymmetric aggregation operators and through numerical applications.