Abstract: Recently, the concept of generalized entropy has been proposed in the literature of information theory. In the present paper, we introduce and study the notion of generalized entropy in the interval (t₁, t₂) as an uncertainty measure. It is shown that the suggested information measure uniquely determines the distribution function. Also, its properties has been studied. Some results have been obtained and some distributions such as uniform, exponential, Pareto, power series and finite range have been characterized by doubly truncated (interval) generalized entropy. Further, we describe a few orders based on this entropy and show its properties.