Abstract
Dempster-Shafer evidence theory (DST) has shown its great advantages to tackle uncertainty in a wide variety of applications. However, how to quantify the information-based uncertainty of basic probability assignment (BPA) with belief entropy in DST framework is still an open issue. The main work of this study is to define a new belief entropy for measuring uncertainty of BPA. The proposed belief entropy has two components. The first component is based on the summation of the probability mass function (PMF) of single events contained in each BPA, which are obtained using plausibility transformation. The second component is the same as the weighted Hartley entropy. The two components could effectively measure the discord uncertainty and non-specificity uncertainty found in DST framework, respectively. The proposed belief entropy is proved to satisfy the majority of the desired properties for an uncertainty measure in DST framework. In addition, when BPA is probability distribution, the proposed method could degrade to Shannon entropy. The feasibility and superiority of the new belief entropy is verified according to the results of numerical experiments.
Highlights
Dempster-Shafer evidence theory (DST) [1,2], which was initially introduced by Dempster in the context of statistical inference and extended by Shafer into a general framework, has drawn great and continued attention in recent years [3,4,5,6]
The main contribution is that a new belief entropy is proposed to quantify the uncertainty of basic probability assignment (BPA)
The proposed belief entropy is comprised of the discord uncertainty measurement and the non-specificity uncertainty measurement
Summary
Dempster-Shafer evidence theory (DST) [1,2], which was initially introduced by Dempster in the context of statistical inference and extended by Shafer into a general framework, has drawn great and continued attention in recent years [3,4,5,6]. Many attempts have been made to extend the Shannon entropy for measuring the uncertainty of BPA in the framework of DST, including Dubois and Prade’s weighted Hartley entropy [33], Höhle’s confusion uncertainty measure [34], Yager’s dissonance uncertainty measure [35], Klir and Ramer’s discord uncertainty measure [36], Klir and Parviz’s strife uncertainty measure [37], Jousselme’s ambiguity uncertainty measure [38], and Deng entropy [39] Speaking, these approaches could degenerate to Shannon entropy if the probability values are assigned to single events. Thereafter, they define a belief entropy, which could verify six desired properties [41] Their approach uses the probability mass function (PMF) transformed by plausibility transformation and weighted Hartley entropy to measure the discord and non-specificity uncertainty, respectively.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
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 call
