Doubly truncated data are sometimes encountered in several applications, mainly in survival and astronomical data analysis. This occurs when the data falls between two points. In this study, we focus on the Shannon entropy measure of doubly truncated random variables. We propose ordering and various aging properties based on this measure. Characterizations of some useful life distributions are obtained. It is showed that under certain condition, the proposed measure determines the distribution function uniquely. Some results on discrete distributions are presented. Finally, applications are given. © 2020 The Authors. Published by Atlantis Press SARL. This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).