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.
Highlights
Dempster–Shafer evidence theory [1,2] has been a useful theory for dealing with uncertainty information
The results present a body of evidence (BOE) listed as follows: m1 : m1 ({ a1, a2, · · ·, a10 }) = 0.4, m1 ({ a10, a11, · · ·, a20 }) = 0.6, m2 : m2 ({ a1, a2, · · ·, a10 }) = 0.4, m2 ({ a1, a2, · · ·, a5, a16, a17, · · ·, a20 }) = 0.6
Deng entropy is a useful method for measuring the uncertainty of basic probability assignment (BPA) in Dempster–Shafer evidence, there are some limitations
Summary
Dempster–Shafer evidence theory [1,2] has been a useful theory for dealing with uncertainty information. For measuring the uncertainty of Dempster–Shafer evidence theory, Shannon entropy theory can’t be applied because a mass function is a generalized probability, which is assigned on the power set of FOD in Dempster–Shafer evidence theory [30]. Deng entropy only considers the BPA of the evidence and the cardinality of the element of the BPA, without the scale of FOD. Zhou et al [36], Pan et al [37] and Cui et al [38] modified Deng entropy, respectively In three references, they all consider the scale of FOD and the relative scale between a focal element of FOD with itself.
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