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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, possibility and imprecise probability theories. First introduced by Arthur P. Dempster 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.〔Shafer, Glenn; ''A Mathematical Theory of Evidence'', Princeton University Press, 1976, ISBN 0-608-02508-9〕 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.〔Kari Sentz and Scott Ferson (2002); (''Combination of Evidence in Dempster–Shafer Theory'' ), Sandia National Laboratories SAND 2002-0835〕 The early contributions have also been the starting points of many important developments, including the Transferable Belief Model and the Theory of Hints.〔 ==Overview== Dempster–Shafer theory is a generalization of the Bayesian theory of subjective probability. Belief functions base degrees of belief (or confidence, or trust) for one question on the probabilities for a related question. The degrees of belief itself may or may not have the mathematical properties of probabilities; how much they differ depends on how closely the two questions are related.〔Shafer, Glenn; (''Dempster–Shafer theory'' ), 2002〕 Put another way, it is a way of representing epistemic plausibilities but it can yield answers that contradict those arrived at using probability theory. Often used as a method of sensor fusion, Dempster–Shafer theory is based on two ideas: obtaining degrees of belief for one question from subjective probabilities for a related question, and Dempster's rule〔Dempster, Arthur P.; ''A generalization of Bayesian inference'', Journal of the Royal Statistical Society, Series B, Vol. 30, pp. 205–247, 1968〕 for combining such degrees of belief when they are based on independent items of evidence. In essence, the degree of belief in a proposition depends primarily upon the number of answers (to the related questions) containing the proposition, and the subjective probability of each answer. Also contributing are the rules of combination that reflect general assumptions about the data. In this formalism a degree of belief (also referred to as a mass) is represented as a belief function rather than a Bayesian probability distribution. Probability values are assigned to ''sets'' of possibilities rather than single events: their appeal rests on the fact they naturally encode evidence in favor of propositions. Dempster–Shafer theory assigns its masses to all of the non-empty subsets of the propositions that compose a system. (In set-theoretic terms, the Power set of the propositions.) For instance, assume a situation where there are two related questions, or propositions, in a system. In this system, any belief function assigns mass to the first proposition, the second, both or neither. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dempster–Shafer theory」の詳細全文を読む スポンサード リンク
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