Editing Dempster–Shafer theory (section)

{{Short description|Mathematical framework to model epistemic uncertainty}}
[[File:Dempster in Brest.JPG|thumb|[[Arthur P. Dempster]] at the Workshop on Theory of Belief Functions ([[Brest, France|Brest]], 1 April 2010).]]

The '''theory of belief functions''', also referred to as '''evidence theory''' or '''Dempster–Shafer theory''' ('''DST'''), is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as [[probability]]<ref 
 name="xu2025">{{cite journal |last1=Xu |first1=Dong-Ling |last2=Yang |first2=Jian-Bo |last3=Wang |first3=Ying-Ming |title=Make Evidence Theory Probabilistic Again |journal=Journal of Control and Decision |date=2025 |pages=1-16 |doi=10.1080/23307706.2025.2495805 |url=https://www.tandfonline.com/doi/epdf/10.1080/23307706.2025.2495805?needAccess=true}}</ref>, [[possibility theory|possibility]] and [[imprecise probability | imprecise probability theories]]. First introduced by [[Arthur P. Dempster]]<ref>{{cite journal|doi=10.1214/aoms/1177698950|title=Upper and lower probabilities induced by a multivalued mapping|journal=The Annals of Mathematical Statistics|year=1967|first=A. P.|last=Dempster|volume=38|issue=2|pages=325–339|doi-access=free}}</ref> in the context of [[statistical inference]], the theory was later developed by [[Glenn Shafer]] into a general framework for modeling epistemic uncertainty—a mathematical theory of [[evidence]].<ref name="SH76">Shafer, Glenn; ''A Mathematical Theory of Evidence'', Princeton University Press, 1976, {{ISBN|0-608-02508-9}}</ref><ref>{{cite journal|author=Fine, Terrence L.|title=Review: Glenn Shafer, ''A mathematical theory of evidence''|journal=Bull. Amer. Math. Soc.|year=1977|volume=83|issue=4|pages=667–672|url=http://projecteuclid.org/euclid.bams/1183538896|doi=10.1090/s0002-9904-1977-14338-3|doi-access=free}}</ref> The theory allows one to combine evidence from different sources and arrive at a degree of belief (represented by a mathematical object called ''belief function'') that takes into account all the available evidence.

In a narrow sense, the term Dempster–Shafer theory refers to the original conception of the theory by Dempster and Shafer. However, it is more common to use the term in the wider sense of the same general approach, as adapted to specific kinds of situations. In particular, many authors have proposed different rules for combining evidence, often with a view to handling conflicts in evidence better.<ref name=Sentz-Ferson>Kari Sentz and Scott Ferson (2002); [https://www.osti.gov/servlets/purl/800792 ''Combination of Evidence in Dempster–Shafer Theory''], Sandia National Laboratories SAND 2002-0835</ref> The early contributions have also been the starting points of many important developments, including the [[transferable belief model]] and the theory of hints.<ref name="KM95" />