A unified formulation of entropy and its application

Abstract

In this paper, a general formulation of entropy is proposed. It depends on two parameters and includes Shannon, Tsallis and fractional entropy, all as special cases. This measure of information is referred to as fractional Tsallis entropy and some of its properties are then studied. Furthermore, the corresponding entropy in the context of Dempster–Shafer theory of evidence is proposed and referred to as fractional version of Tsallis–Deng entropy. Finally, an application to two classification problems is presented.