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Evidence-based subjective logic : ウィキペディア英語版
Evidence-based subjective logic

Evidence-based subjective logic (EBSL) is a variant 〔B. Skoric, S.J.A. de Hoogh, N. Zannone. ''Flow-based reputation with uncertainty: Evidence-Based Subjective Logic''.
http://link.springer.com/article/10.1007/s10207-015-0298-5 .
http://arxiv.org/abs/1402.3319〕 of subjective logic in which the transitivity of opinions (discounting) is handled by applying weights to the evidence underlying the opinions.
Subjective Logic is based on Dempster–Shafer belief theory.
The discounting rule in EBSL makes it possible to handle arbitrary trust networks.
==Relation between evidence and opinions==
Consider a proposition P.
Let ''p'' be the amount of evidence supporting P, and ''n'' the amount of evidence supporting ¬P. We write the evidence as a vector (''p'', ''n''). Let ''c'' be a positive constant representing a "unit" of evidence. An opinion (''b'', ''d'', ''u'') is formed on the basis of the evidence (''p'', ''n''). There is a one-to-one mapping between the opinion and the evidence,
:
(b,d,u)=\frac
\quad\quad
(p,n)=c\frac.
\quad\quad (1)

In the original literature on subjective logic the constant was set to
''c'' = 2.
The mapping (1) is the unique solution of the following set of constraints,〔
*''b''/''d'' = ''p''/''n''.
*''b'' + ''d'' + ''u'' = 1.
*''p'' + ''n'' = 0 implies ''u'' = 1.
*p\to\infty implies u\to 0.
Alternatively, (1) can be derived from an analysis of
a posteriori probability
distributions〔A. Jøsang. A Logic for Uncertain Probabilities. ''International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems.'' 9(3), pp. 279–311, June 2001. (PDF )〕
(beta distributions).
There are three "corner points" in opinion space:
the full Belief B = (1,0,0),
the full Disbelief D = (0,1,0),
and full Uncertainty U = (0,0,1).
Opinions on the line between B and D (including B and D) are called "dogmatic opinions". They have zero uncertainty, which is achievable only with an infinite amount of evidence. Dogmatic opinions are often excluded from the algebra.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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