On the handing of one-side-triangle-fuzzy-number-valued attributes in decision tree generation

We present a result applicable to classification algorithm that generate decision trees or rules using the information entropy minimization heuristic for discretizing one-side-triangle-fuzzy-number-valued attributes. The results serves to give a better understanding of the entropy measure, to point out that the behavior of the information entropy heuristic possesses desirable properties that justify its usage in a formal sense, and to improve the efficiency of evaluating one-side-triangle-fuzzy-number-valued attributes for cut value selection. Along with the formal proof, we present empirical results that demonstrate the theoretically expected reduction evaluation effort for training data sets from real-world domains.