In machine learning, monotone classification is concerned with a classification function to learn in order to guarantee a kind of monotonicity of the class with respect to attribute values. In this paper, we focus on rank discrimination measures to be used in decision tree induction, i.e., functions able to measure the discrimination power of an attribute with respect to the class taking into account the monotonicity of the class with respect to the attribute. Three new measures are studied in detail and an experimental analysis is also provided, comparing the proposed approach with other well-known monotone and non-monotone classifiers in terms of classification accuracy.