Abstract
How to quantify the uncertain information in the framework of Dempster-Shafer evidence theory is still an open issue. Quite a few uncertainty measures have been proposed in Dempster-Shafer framework, however, the existing studies mainly focus on the mass function itself, the available information represented by the scale of the frame of discernment (FOD) in the body of evidence is ignored. Without taking full advantage of the information in the body of evidence, the existing methods are somehow not that efficient. In this paper, a modified belief entropy is proposed by considering the scale of FOD and the relative scale of a focal element with respect to FOD. Inspired by Deng entropy, the new belief entropy is consistent with Shannon entropy in the sense of probability consistency. What’s more, with less information loss, the new measure can overcome the shortage of some other uncertainty measures. A few numerical examples and a case study are presented to show the efficiency and superiority of the proposed method.
Highlights
Dempster-Shafer evidence theory [1, 2] is effective in modeling and processing uncertain information of intelligent systems
The exponential factor e jXj in the new belief entropy represents the uncertain information in a body of evidence (BOE) that has been ignored by Deng entropy and some other uncertainty measures such as the confusion measure, the dissonance measure, the weighted Hartley entropy, the discord measure and the strife measure
In Example 4.3, the uncertain degree indicated by the new belief entropy is smaller than that of Deng entropy, this is achieved by taking into consideration of the scale of the frame of discernment (FOD) in the BOE
Summary
Dempster-Shafer evidence theory [1, 2] is effective in modeling and processing uncertain information of intelligent systems. Shannon entropy can’t be used directly in the framework of Dempster–Shafer evidence theory, because a mass function in evidence theory is a generalized probability assigned on the power set of FOD To address this issue, some modified methods based on Shannon entropy are proposed [49,50,51,52,53], of which some have been successfully applied in real applications [66, 67].
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
