Several fuzzy extensions of decision tree induction, which is an established machine-learning method, have already been proposed in the literature. So far, however, fuzzy decision trees have almost exclusively been used for the performance task of classification. In this paper, we show that a fuzzy extension of decision trees is arguably more useful for another performance task, namely ranking. Roughly, the goal of ranking is to order a set of instances from most likely positive to most likely negative. The motivation for applying fuzzy decision trees to this problem originates from recent investigations of the ranking performance of conventional decision trees. These investigations will be continued and complemented in this paper. Our results reveal some properties that seem to be crucial for a good ranking performance-properties that are better and more naturally offered by fuzzy than by conventional decision trees. Most notably, a fuzzy decision tree produces scores in terms of membership degrees on a fine-granular scale. Using these membership degrees as a ranking criterion, a key problem of conventional decision trees is solved in an elegant way, namely the question of how to break ties between instances in the same leaf or, more generally, between equally scored instances.
- Area under the receiver operating characteristic (ROC) curve
- bipartite ranking
- decision trees
- fine-granular membership degrees
- fuzzy inference
- Laplace correction
- soft feature splits