Some properties of the exponential entropy

Abstract A new definition of probabilistic entropy based on the exponential behavior of gain function has recently been introduced by the authors 1. [1]. It has also been extended to define various image entropy measures 2. [2]and hybrid and higher order entropy of fuzzy sets 3. [3]. The present work investigates some additional properties (in the light of both probability theory and fuzzy set theory) of this new entropy definition to ensure its greater range of applications.