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On cumulative belief entropy

Cumulative residual entropy and cumulative entropy are new methods based on the cumulative distribution of random variables and could be used to correctly measure the uncertainty of information in probability theory. However, how to determine the uncertain degree is also an open issue in Dempster-Shafer evidence theory (D-S evidence theory), even though there are different kinds of methods now, but they have not considered about the cumulative effect of the belief probability assignment (BPA), so we refer to the cumulative idea and consider about the relationship between the probability theory and evidence theory so that the structure could be transformed to belief intervals of the single subsets, then comprehensively think about the belief function Bel and the plausibility function Pl which as the limitations. As a result, a new method to ascertain the uncertain degree of the information is presented in the background of D-S evidence theory, some numerical analysis and comparative analysis are performed in order to demonstrate the new cumulative belief entropy could provide a optimistic way of measuring the uncertain degree and the results received are in line with expectations well.