Splitting Rules for Monotone Fuzzy Decision Trees

This paper considers the problem of building monotone fuzzy decision trees when the attributes and the labeling function are in the form of partitions (in Ruspini’s sense) of totally ordered labels. We define a fuzzy version of Shannon and Gini rank discrimination measures, based on a definition of fuzzy dominance, to be used in the splitting phase of a fuzzy decision tree inductive construction algorithm. These extensions generalize the rank discrimination measures introduced in previous work. Afterwards, we introduce a new algorithm to build a fuzzy decision tree enforcing monotonicity and we present an experimental analysis on an artificial data set.