Based on axiomatic fuzzy set (AFS) theory and fuzzy information entropy, a novel fuzzy oblique decision tree (FODT) algorithm is proposed in this paper. Traditional axis-parallel decision trees only consider a single feature at each non-leaf node, while oblique decision trees partition the feature space with an oblique hyperplane. By contrast, the FODT takes dynamic mining fuzzy rules as a decision function. The main idea of the FODT is to use these fuzzy rules to construct leaf nodes for each class in each layer of the tree; the samples that cannot be covered by the fuzzy rules are then put into an additional node – the only non-leaf node in this layer. Construction of the FODT consists of four major steps: (a) generation of fuzzy membership functions automatically by AFS theory according to the raw data distribution; (b) extraction of dynamically fuzzy rules in each non-leaf node by the fuzzy rule extraction algorithm (FREA); (c) construction of the FODT by the fuzzy rules obtained from step (b); and (d) determination of the optimal threshold to generate a final tree. Compared with five traditional decision trees (C4.5, LADtree (LAD), Best-first tree (BFT), SimpleCart (SC) and NBTree (NBT)) and a recently obtained fuzzy rules decision tree (FRDT) on eight UCI machine learning data sets and one biomedical data set (ALLAML), the experimental results demonstrate that the proposed algorithm outperforms the other decision trees in both classification accuracy and tree size.
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