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author:

Xu, D.-L. (Xu, D.-L..) [1] | Yang, J.-B. (Yang, J.-B..) [2] | Wang, Y.-M. (Wang, Y.-M..) [3]

Indexed by:

Scopus

Abstract:

In this paper, we prove from a new angle that Dempster’s rule is inherently probabilistic, extends Bayes’ rule and reduces to Bayes’ rule when precise probabilities are available, regardless of whether prior is uniform. We use examples to demonstrate this equivalence. Additionally, we explain that the Evidential Reasoning (ER) rule is also probabilistic and includes Bayes’ and Dempster’s rules as special cases. Furthermore, we address some criticisms of the behaviour of Dempster’s rule from a probabilistic perspective and explain the rationality of the behaviour. We also identify instances where such critiques were misapplied. Finally, we clarify vital differences between belief degrees in belief functions and basic probabilities and highlight the critical differences between Shafer’s discounting method and the ER rule. These differences make the latter probabilistic, while the former is not. Our motivation is to show that evidence theory has a probabilistic foundation and is possible to become probabilistic again. © 2025 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

Keyword:

Bayesian inference Evidence theory evidential reasoning inference under uncertainty inference with imperfect data probabilistic reasoning

Community:

  • [ 1 ] [Xu D.-L.]Alliance Manchester Business School, The University of Manchester, Manchester, United Kingdom
  • [ 2 ] [Yang J.-B.]Alliance Manchester Business School, The University of Manchester, Manchester, United Kingdom
  • [ 3 ] [Wang Y.-M.]Department of Management Science and Engineering, School of Economics and Management, Fuzhou University, Fuzhou, China

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Source :

Journal of Control and Decision

ISSN: 2330-7706

Year: 2025

1 . 5 0 0

JCR@2023

Cited Count:

WoS CC Cited Count:

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ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 1

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