Fusing Fuzzy Monotonic Decision Trees

Ordinal classification is an important classification task, in which there exists a monotonic constraint between features and the decision class. In this article, we aim to develop a method of fusing ordinal decision trees with fuzzy rough-set-based attribute reduction. Most of the existing attribute reduction methods for ordinal decision tables are based on the dominance rough set theory or significance measures. However, the crisp dominance relation is difficult in making full use of the information of attribute values; and the reducts based on significance measures are poor in interpretability and may contain unnecessary attributes. In this article, we first define a discernibility matrix with fuzzy dominance rough set. With this discernibility matrix, multiple reducts can be found, which provide multiple complementary feature subspaces with original information. Then, diverse ordinal trees can be established from these feature subspaces, and finally, the trees are fused by majority voting. The experimental results show that the proposed fusion method performs significantly better than other fusion methods using dominance rough set or significance measures.