A Correction to this paper has been published: https://doi.org/10.1038/s41567-021-01261-9.

This paper examines the relationship between Shafer's belief functions and convex sets of probability distributions. Kyburg's (1986) result showed that belief function models form a subset of the class of closed convex probability distributions. This paper emphasizes the importance of Kyburg's result by looking at simple examples involving Bernoulli trials. Furthermore, it is shown that many co...

A sufficient condition is developed for the equality of the plausibility and commonality measures of the Dempster-Shafer belief calculus. When the condition is met, as it is in many applications, an efficient method to calculate relative plausibility is available. In particular, the method can be used to calculate the relative plausibility of atomic hypotheses and, therefore, it can be used to ...

Picture fuzzy set is the most widely used tool to handle uncertainty with account of three membership degrees, namely, positive, negative, and neutral such that their sum bound up 1. It generalization existing intuitionistic sets. This paper studies interval probability problems picture sets belief structure. The function a vital represent uncertain information in more effective manner. On othe...

The Dempster-Shafer “theory of evidence” encompasses and extends the Bayes Theorem-based decision making machinery. Dempster-Shafer’s innovation is the introduction of lower and upper bounds, designated “belief” and “plausibility”, that are attached to probability estimates. The Dempster-Shafer algebra provides for propagation of and reasoning about these quantities according to an algebra whos...

This paper presents a supervised classi®cation model integrating fuzzy reasoning and Dempster±Shafer propagation of evidence has been built on top of connectionist techniques to address classi®cation tasks in which vagueness and ambiguity coexist. The salient aspect of the approach is the integration within a neuro-fuzzy system of knowledge structures and inferences for evidential reasoning bas...

Cognitive radio (CR) is a promising technology that brings about remarkable improvement in spectrum utilization. To tackle the hidden terminal problem, cooperative spectrum sensing (CSS) which benefits from the spatial diversity has been studied extensively. Since CSS is vulnerable to the attacks initiated by malicious secondary users (SUs), several secure CSS schemes based on Dempster-Shafer t...