A hybrid monotone decision tree model for interval-valued attributes

The existing monotonic decision tree algorithms are based on a linearly ordered constraint that certain attributes are monotonously consistent with the decision, which could be called monotonic attributes, whereas others, called non-monotonic attributes. In practice, monotonic and non-monotonic attributes coexist in most classification tasks, and some attribute values are even evaluated as interval numbers. In this paper, we proposed a fuzzy rank-inconsistent rate based on probability degree to judge the monotonicity of interval numbers. Furthermore, we devised a hybrid model composed of monotonic and non-monotonic attributes to construct a mixed monotone decision tree for interval-valued data. Experiments on artificial and real-world data sets show that the proposed hybrid model is effective.