Editing Dempster–Shafer theory (section)

====Example producing counter-intuitive results in case of high conflict====
An example with exactly the same numerical values was introduced by [[Lotfi Zadeh]] in 1979,<ref name="Zadeh79">L. Zadeh, On the validity of Dempster's rule of combination, Memo M79/24, Univ. of California, Berkeley, USA, 1979</ref><ref name="Zadeh84">L. Zadeh, Book review: A mathematical theory of evidence, The Al Magazine, Vol. 5, No. 3, pp. 81–83, 1984</ref><ref name="Zadeh86">L. Zadeh, [https://wvvw.aaai.org/ojs/index.php/aimagazine/article/download/542/478 A simple view of the Dempster–Shafer Theory of Evidence and its implication for the rule of combination] {{Webarchive|url=https://web.archive.org/web/20190728221641/https://wvvw.aaai.org/ojs/index.php/aimagazine/article/download/542/478 |date=2019-07-28 }}, The Al Magazine, Vol. 7, No. 2, pp. 85–90, Summer 1986.</ref>
to point out counter-intuitive results generated by Dempster's rule when there is a high degree of conflict. The example goes as follows:

:Suppose that one has two equi-reliable doctors and one doctor believes a patient has either a brain tumor, with a probability (i.e. a basic belief assignment—bba's, or mass of belief) of 0.99; or meningitis, with a probability of only 0.01. A second doctor believes the patient has a concussion, with a probability of 0.99, and believes the patient suffers from meningitis, with a probability of only 0.01. Applying  Dempster's rule to combine these two sets of masses of belief, one gets finally ''m''(meningitis)=1 (the meningitis is diagnosed with 100 percent of confidence).

Such result goes against common sense since both doctors agree that there is a little chance that the patient has a meningitis. This example has been the starting point of many research works for trying to find a solid justification for Dempster's rule and for foundations of Dempster–Shafer theory<ref name="Ruspini88">E. Ruspini, "[https://www.researchgate.net/profile/Enrique_Ruspini/publication/243627217_The_Logical_Foundations_of_Evidential_Reasoning/links/55ce0d6408ae502646a73338/The-Logical-Foundations-of-Evidential-Reasoning.pdf The logical foundations of evidential reasoning]", ''SRI Technical Note'' '''408''', December 20, 1986 (revised April 27, 1987)</ref><ref name="Wilson93">N. Wilson, "[https://arxiv.org/abs/1303.1518 The assumptions behind Dempster's rule]", in ''Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence'', pages 527–534, Morgan Kaufmann Publishers, San Mateo, CA, USA, 1993</ref> or to show the inconsistencies of this theory.<ref name="Voorbraak88">F. Voorbraak, "[https://dspace.library.uu.nl/bitstream/handle/1874/26413/Preprint_no_42.pdf?sequence=1 On the justification of Dempster's rule of combination]", ''Artificial Intelligence'', Vol. '''48''', pp. 171–197, 1991</ref><ref name="Wang1994">Pei Wang, "[https://arxiv.org/abs/1302.6849 A Defect in Dempster–Shafer Theory]", in ''Proceedings of the 10th Conference on Uncertainty in Artificial Intelligence'', pages 560–566, Morgan Kaufmann Publishers, San Mateo, CA, USA, 1994</ref><ref name="Walley91">P. Walley, "[https://philarchive.org/rec/WALSRW?fId=&eId=WALSRW&gId=&cId=&tSort=ct+desc Statistical Reasoning with Imprecise Probabilities]{{Dead link|date=January 2024 |bot=InternetArchiveBot |fix-attempted=yes }}", Chapman and Hall, London, pp. 278–281, 1991</ref>