Towards Dynamical Systems Approach to Fuzzy Clustering

In many application areas, there is a need for clustering, and there is a need to take fuzzy uncertainty into account when clustering. Most existing fuzzy clustering techniques are based on the idea that an object belongs to a certain cluster if this object is close to a typical object from this cluster. In some application areas, however, this idea does not work well. One example of such application is clustering in education that is used to convert a detailed number grade into a letter grade. In such application, it is more appropriate to use clustering techniques which are based on a different idea: that an object tends to belong to the same cluster as its nearest neighbor. In this paper, we explain the relationship between this idea and dynamical systems, and we discuss how fuzzy uncertainty can be taken into account in this approach to clustering