In clustering process, fuzzy partition performs better than hard partition when the boundaries between clusters are vague. Whereas, traditional fuzzy clustering algorithms produce less interpretable results, limiting their application in security, privacy, and ethics fields. To that end, this paper proposes an interpretable fuzzy clustering algorithm—fuzzy decision tree-based clustering which combines the flexibility of fuzzy partition with the interpretability of the decision tree. We constructed an unsupervised multi-way fuzzy decision tree to achieve the interpretability of clustering, in which each cluster is determined by one or several paths from the root to leaf nodes. The proposed algorithm comprises three main modules: feature and cutting point-selection, node fuzzy splitting, and cluster merging. The first two modules are repeated to generate an initial unsupervised decision tree, and the final module is designed to combine similar leaf nodes to form the final compact clustering model. Our algorithm optimizes an internal clustering validation metric to automatically determine the number of clusters without their initial positions. The synthetic and benchmark datasets were used to test the performance of the proposed algorithm. Furthermore, we provided two examples demonstrating its interest in solving practical problems.

In this paper, a rule learning method based on interval-constrained clustering is proposed to efficiently design a compact belief rule-based classifier. The main idea of this method is to learn a compact belief rule base based on a set of prototypes generated from the original training set. First, an interval-constrained clustering algorithm is used to divide the training data for each class into several clusters, with which the number of data belonging to each cluster can be constrained within a given interval. Then, we define a belief rule based on the centroid of each cluster. Finally, a two-objective optimization procedure is designed to get a compact belief rule base with a better trade-off between accuracy and interpretability. Two experiments based on synthetic and benchmark data sets have been carried out to evaluate the performance of the proposed classifier.