Fuzzy clustering model based on changes in vagueness

This paper proposes a fuzzy clustering model to extract the exact changes of vagueness in data, which are observed as similarities of objects over time. That is, the objective data is assumed to have vagueness, which changes over time. The author regards this data as 3-way data. For such 3-way data, the most difficult problem has been that the optimal solutions at different times are in conflict with one another. In order to solve this problem, conventional methods have used parameters to represent the weights of clusters at different times. However, in such a case, we cannot see the exact change in vagueness. So the author proposes a clustering model for defining situations of dynamic change. The vagueness of an observation is defined by convex and normal fuzzy sets (CNF sets), and defines a conical membership function to represent the CNF sets. The dissimilarity between two observations is defined as a fuzzy asymmetric dissimilarity. An asymmetric aggregation operator is considered. Numerical results from an application validity the proposed model.