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170
The Transferable Belief Model
 ARTIFICIAL INTELLIGENCE
, 1994
"... We describe the transferable belief model, a model for representing quantified beliefs based on belief functions. Beliefs can be held at two levels: (1) a credal level where beliefs are entertained and quantified by belief functions, (2) a pignistic level where beliefs can be used to make decisions ..."
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Cited by 489 (16 self)
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We describe the transferable belief model, a model for representing quantified beliefs based on belief functions. Beliefs can be held at two levels: (1) a credal level where beliefs are entertained and quantified by belief functions, (2) a pignistic level where beliefs can be used to make decisions and are quantified by probability functions. The relation between the belief function and the probability function when decisions must be made is derived and justified. Four paradigms are analyzed in order to compare Bayesian, upper and lower probability, and the transferable belief approaches.
Conditional Reasoning with Subjective Logic
 JOURNAL OF MULTIPLEVALUED LOGIC AND SOFT COMPUTING 15(1):PP. 538
, 2008
"... Conditional inference plays a central role in logical and Bayesian reasoning, and is used in a wide range of applications. It basically consists of expressing conditional relationship between parent and child propositions, and then to combine those conditionals with evidence about the parent proposi ..."
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Cited by 63 (16 self)
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Conditional inference plays a central role in logical and Bayesian reasoning, and is used in a wide range of applications. It basically consists of expressing conditional relationship between parent and child propositions, and then to combine those conditionals with evidence about the parent propositions in order to infer conclusions about the child propositions. While conditional reasoning is a well established part of classical binary logic and probability calculus, its extension to belief theory has only recently been proposed. Subjective opinions represent a special type of general belief functions. This article focuses on conditional reasoning in subjective logic where beliefs are represented in the form of binomial or multinomial subjective opinions. Binomial conditional reasoning operators for subjective logic have been defined in previous contributions. We extend this approach to multinomial opinions, thereby making it possible to represent conditional and evidence opinions on frames of arbitrary size. This makes subjective logic a powerful tool for conditional reasoning in situations involving ignorance and partial information, and makes it possible to analyse Bayesian network models with uncertain probabilities.
Data Fusion in the Transferable Belief Model.
, 2000
"... When Shafer introduced his theory of evidence based on the use of belief functions, he proposed a rule to combine belief functions induced by distinct pieces of evidence. Since then, theoretical justifications of this socalled Dempster's rule of combination have been produced and the meaning of ..."
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Cited by 52 (0 self)
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When Shafer introduced his theory of evidence based on the use of belief functions, he proposed a rule to combine belief functions induced by distinct pieces of evidence. Since then, theoretical justifications of this socalled Dempster's rule of combination have been produced and the meaning of distinctness has been assessed. We will present practical applications where the fusion of uncertain data is well achieved by Dempster's rule of combination. It is essential that the meaning of the belief functions used to represent uncertainty be well fixed, as the adequacy of the rule depends strongly on a correct understanding of the context in which they are applied. Missing to distinguish between the upper and lower probabilities theory and the transferable belief model can lead to serious confusion, as Dempster's rule of combination is central in the transferable belief model whereas it hardly fits with the upper and lower probabilities theory. Keywords: belief function, transferable beli...
Conjunctive and Disjunctive Combination of Belief Functions Induced by Non Distinct Bodies of Evidence
 ARTIFICIAL INTELLIGENCE
, 2007
"... Dempster’s rule plays a central role in the theory of belief functions. However, it assumes the combined bodies of evidence to be distinct, an assumption which is not always verified in practice. In this paper, a new operator, the cautious rule of combination, is introduced. This operator is commuta ..."
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Cited by 34 (10 self)
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Dempster’s rule plays a central role in the theory of belief functions. However, it assumes the combined bodies of evidence to be distinct, an assumption which is not always verified in practice. In this paper, a new operator, the cautious rule of combination, is introduced. This operator is commutative, associative and idempotent. This latter property makes it suitable to combine belief functions induced by reliable, but possibly overlapping bodies of evidence. A dual operator, the bold disjunctive rule, is also introduced. This operator is also commutative, associative and idempotent, and can be used to combine belief functions issues from possibly overlapping and unreliable sources. Finally, the cautious and bold rules are shown to be particular members of infinite families of conjunctive and disjunctive combination rules based on triangular norms and conorms.
Decision Making in a Context where Uncertainty is Represented by Belief Functions.
, 2000
"... A quantified model to represent uncertainty is incomplete if its use in a decision environment is not explained. When belief functions were first introduced to represent quantified uncertainty, no associated decision model was proposed. Since then, it became clear that the belief functions meani ..."
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Cited by 30 (4 self)
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A quantified model to represent uncertainty is incomplete if its use in a decision environment is not explained. When belief functions were first introduced to represent quantified uncertainty, no associated decision model was proposed. Since then, it became clear that the belief functions meaning is multiple. The models based on belief functions could be understood as an upper and lower probabilities model, as the hint model, as the transferable belief model and as a probability model extended to modal propositions. These models are mathematically identical at the static level, their behaviors diverge at their dynamic level (under conditioning and/or revision). For decision making, some authors defend that decisions must be based on expected utilities, in which case a probability function must be determined. When uncertainty is represented by belief functions, the choice of the appropriate probability function must be explained and justified. This probability function doe...
Target Identification Based on the Transferable Belief Model Interpretation of DempsterShafer Model. Pars I: Methodology
, 2001
"... This paper explains how multisensor data fusion and target identification can be performed within the transferable belief model, a model for the representation of quantified uncertainty based on belief functions. The paper is presented in two parts: methodology and application. In this part, we pres ..."
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Cited by 30 (5 self)
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This paper explains how multisensor data fusion and target identification can be performed within the transferable belief model, a model for the representation of quantified uncertainty based on belief functions. The paper is presented in two parts: methodology and application. In this part, we present the underlying theory, in particular the General Bayesian Theorem needed to transform likelihoods into beliefs and the pignistic transformation needed to build the probability measure required for decision making. We end with a simple example. More sophisticated examples and some comparative studies are presented in Part II. The results presented here can be extended directly to many problems of data fusion and diagnosis.
Multisensor triplet Markov chains and theory of evidence
 International Journal of Approximate Reasoning
, 2006
"... Hidden Markov chains (HMC) are widely applied in various problems occurring in different areas like Biosciences, Climatology, Communications, Ecology, Econometrics and Finances, Image or Signal processing. In such models, the hidden process of interest X is a Markov chain, which must be estimated fr ..."
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Cited by 30 (13 self)
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Hidden Markov chains (HMC) are widely applied in various problems occurring in different areas like Biosciences, Climatology, Communications, Ecology, Econometrics and Finances, Image or Signal processing. In such models, the hidden process of interest X is a Markov chain, which must be estimated from an observable Y, interpretable as being a noisy version of X. The success of HMC is mainly due to the fact that the conditional probability distribution of the hidden process with respect to the observed process remains Markov, which makes possible different processing strategies such as Bayesian restoration. HMC have been recently generalized to ‘‘Pairwise’ ’ Markov chains (PMC) and ‘‘Triplet’ ’ Markov chains (TMC), which offer similar processing advantages and superior modeling capabilities. In PMC, one directly assumes the Markovianity of the pair (X, Y) and in TMC, the distribution of the pair (X, Y) is the marginal distribution of a Markov process (X, U, Y), where U is an auxiliary process, possibly contrived. Otherwise, the Dempster–Shafer fusion can offer interesting extensions of the calculation of the ‘‘a posteriori’ ’ distribution of the hidden data. The aim of this paper is to present different possibilities of using the Dempster–Shafer fusion in the context of different multisensor Markov models. We show that the posterior distribution remains calculable in different general situations and present some examples of their applications in remote sensing area.
Belief Functions on Real Numbers.
, 2005
"... We generalize the TBM (transferable belief model) to the case where the frame of discernment is the extended set of real numbers R = [−∞, ∞], under the assumptions that ‘masses’ can only be given to intervals. Masses become densities, belief functions, plausibility functions and commonality function ..."
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Cited by 29 (0 self)
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We generalize the TBM (transferable belief model) to the case where the frame of discernment is the extended set of real numbers R = [−∞, ∞], under the assumptions that ‘masses’ can only be given to intervals. Masses become densities, belief functions, plausibility functions and commonality functions become integrals of these densities and pignistic probabilities become pignistic densities. The mathematics of belief functions become essentially the mathematics of probability density functions on R².