Monotonicity is a major property of entropy measures. In this paper, we focus on entropy measures for intuitionistic fuzzy sets and interval-valued fuzzy sets. We consider their polar representation which provides an easy interpretation of monotonicity for several entropy measures introduced in the literature. Moreover, this polar representation enables us to propose two new kinds of monotonicity for such entropies, that offer a more understandable way to explain differences of entropies. Classical measures of entropy for intuitionistic fuzzy sets are compared with regard to these new forms of monotonicity.