Entropies and measures of information are extensively used in several domains and applications in Artificial Intelligence. Among the original quantities from Information theory and Probability theory, a lot of extensions have been introduced to take into account fuzzy sets, intuitionistic fuzzy sets and other representation models of uncertainty and imprecision. In this paper, we propose a study of the common property of monotonicity of such measures with regard to a refinement of information, showing that the main differences between these quantities come from the diversity of orders defining such a refinement. Our aim is to propose a clarification of the concept of refinement of information and the underlying monotonicity, and to illustrate this paradigm by the utilisation of such measures in Artificial Intelligence.