Belief-Based Fuzzy and Imprecise Clustering for Arbitrary Data Distributions

Fuzzy clustering is still a hot topic because it can calculate the support degrees of an object belonging to different clusters to characterize uncertainty. However, it remains a challenge to detect clusters of arbitrary shapes, sizes, and dimensionality. What is worse, some objects are indistinguishable (imprecise) when they are in the overlapping regions of different clusters. To address such issues, this article investigates a belief-based fuzzy and imprecise clustering (BFI) method, which can detect arbitrary clusters and provide the behavior (support) of objects to these clusters. Moreover, BFI can assign each imprecise object to a meta-cluster, defined as the union of specific clusters, to characterize (partial) imprecision. The proposed BFI can significantly reduce the risk of misclassification, and the effectiveness is validated in image processing (e.g., image segmentation and classification) and several benchmark datasets by comparing it with some typical methods.