A New Belief Entropy Based on Deng Entropy

Abstract

For Dempster–Shafer evidence theory, how to measure the uncertainty of basic probability assignment (BPA) is still an open question. Deng entropy is one of the methods for measuring the uncertainty of Dempster–Shafer evidence. Recently, some limitations of Deng entropy theory are found. For overcoming these limitations, some modified theories are given based on Deng entropy. However, only one special situation is considered in each theory method. In this paper, a unified form of the belief entropy is proposed on the basis of Deng entropy. In the new proposed method, the scale of the frame of discernment (FOD) and the relative scale of a focal element with reference to FOD are considered. Meanwhile, for an example, some properties of the belief entropy are obtained based on a special situation of a unified form. Some numerical examples are illustrated to show the efficiency and accuracy of the proposed belief entropy.