Fuzzy clustering model for fuzzy data

In a clustering problem in which the observations of the objects are given by the values involving vagueness, the ordinary fuzzy clustering methods are not available. In this paper, these data are treated as fuzzy data which are defined by convex and normal fuzzy sets (CNF sets), and a new fuzzy clustering model for the fuzzy data is proposed. We define a conical membership function to represent the CNF sets, and propose a fuzzy dissimilarity between a pair of fuzzy observations, which is an extension of the fuzzy distance proposed by L.T. Koczy et al. (1993). This dissimilarity, discussed in this paper, becomes asymmetric. Therefore, we obtain two different clustering results with respect to each asymmetric part. To achieve consistent clustering results, an additive fuzzy clustering model is used to obtain a solution by a multicriteria clustering technique