Weighted deng entropy and its application in uncertainty measure

How to quantify the uncertainty information consisted in the body of evidence (BOE) in the framework of Dempster-Shafer evidence theory is still an open issue. A few uncertainty measures have been proposed in Dempster-Shafer evidence theory framework, but these studies mainly focused on the mass function itself and the scale of the frame of discernment (FOD) is totally ignored. Since the existing uncertainty measures do not take full advantage of the information in the BOE, these uncertainty measures are not that efficient in some cases or even cannot present the changing of the information volume in BOE. Based on Deng entropy, this paper presents a new belief entropy named weighted Deng entropy. The weight of the proposed belief entropy is based on the relative scale of a proposition with regard to the FOD. The numerical example shows that the new belief entropy can quantify the uncertainty in mass BOE more accurately, which is helpful for information processing. In addition, the case study based on the weighted Deng entropy shows a vision of the new method in real application.