Hesitant fuzzy decision tree approach for highly imbalanced data classification

Abstract

Fuzzy decision tree algorithms provide one of the most powerful classifiers applied to any kind of data. In this paper, some new Fuzzy Decision Tree (FDT) approaches based on Hesitant Fuzzy Sets (HFSs) have been introduced to classify highly imbalanced data sets. Our proposed classifiers employ k-means clustering algorithm to divide the majority class samples into several clusters. Then, each cluster sample is labeled by a new synthetic class label. After that, five discretization methods (Fayyad, Fusinter, Fixed Frequency, Proportional, and Uniform Frequency) are considered to generate Membership Functions (MFs) of each attribute. Five FDTs are constructed based on five discretization methods Hesitant Fuzzy Information Gain (HFIG) is proposed as a new attribute selection criterion that can be used instead of Fuzzy Information Gain (FIG). HFIG is calculated by aggregating obtained FIGs from different discretization methods by information energy. For predicting the class label of new samples, three aggregation methods are utilized. The combination of splitting criterion (HFIG or FIG), five different discretization methods (for generating MFs) and three aggregation methods (to predict class label of new samples) generate special classifiers for addressing the imbalanced classification. For illustrating the difference between our proposed methods, taxonomy is proposed in the paper that categorizes them in three general categories. The experimental results show that our proposed methods outperform the other fuzzy rule-based approaches over 20 highly imbalanced data sets of KEEL in terms of AUC.