Book ChapterDOI
Constructing the Pignistic Probability Function in a Context of Uncertainty
Philippe Smets
- Vol. 10, pp 29-40
TLDR
The probability function is derived axiomatically the probability function that should be used to make decisions given any form of underlying uncertainty.Abstract:
Summary We derive axiomatically the probability function that should be used to make decisions given any form of underlying uncertainty.read more
Citations
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Journal ArticleDOI
The transferable belief model
TL;DR: The transferable belief model is described, a model for representing quantified beliefs based on belief functions that can be held at two levels: a credal level where beliefs are entertained and quantified by belief functions, and a pignisticlevel where beliefs can be used to make decisions and are quantification by probability functions.
Journal ArticleDOI
The combination of evidence in the transferable belief model
TL;DR: A description of the transferable belief model, which is used to quantify degrees of belief based on belief functions, is given and a set of axioms justifying Dempster's rule for the combination of belief functions induced by two distinct evidences is presented.
Book ChapterDOI
The Transferable Belief Model
TL;DR: Smets, P. and R. Kennes, The transferable belief model, Artificial Intelligence 66 (1994) 191–234.
Journal ArticleDOI
A new distance between two bodies of evidence
TL;DR: A principled distance between two basic probability assignments (BPAs) (or two bodies of evidence) based on a quantification of the similarity between sets is introduced based on the evidential theory of Dempster–Shafer.
Journal ArticleDOI
Decision making in the TBM: the necessity of the pignistic transformation
TL;DR: The origin of the pignistic transformation is justified by a linearity requirement showing it is not ad hoc but unavoidable provides one accepts expected utility theory.
References
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Book
A mathematical theory of evidence
TL;DR: This book develops an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions.
Book
Optimal Statistical Decisions
TL;DR: In this article, the authors present a survey of probability theory in the context of sample spaces and decision problems, including the following: 1.1 Experiments and Sample Spaces, and Probability 2.2.3 Random Variables, Random Vectors and Distributions Functions.
Journal ArticleDOI