This paper describes the integration of a particle filter and a continuous version of the transferable belief model. The output from the particle filter is used as input to the transferable belief model. The transferable belief model's continuous nature allows for the prior knowledge over the classification space to be incorporated within the system. Classification of objects is demonstrated within the paper and compared to the more classical Bayesian classification routine. This is the first time that such an approach has been taken to jointly classify and track targets. We show that there is a great deal of flexibility built into the continuous transferable belief model and in our comparison with a Bayesian classifier, we show that our novel approach offers a more robust classification output that is less influenced by noise

The transferable belief model (TBM) is a model to represent quantified uncertainties based on belief functions, unrelated to any underlying probability model. In this framework, two main approaches to pattern classification have been developed: the TBM model-based classifier, relying on the general Bayesian theorem (GBT), and the TBM case-based classifier, built on the concept of similarity of a pattern to be classified with training patterns. Until now, these two methods seemed unrelated, and their connection with standard classification methods was unclear. This paper shows that both methods actually proceed from the same underlying principle, i.e., the GBT, and that they essentially differ by the nature of the assumed available information. This paper also shows that both methods collapse to a kernel rule in the case of precise and categorical learning data and for certain initial assumptions, and a simple relationship between basic belief assignments produced by the two methods is exhibited in a special case. These results shed new light on the issues of classification and supervised learning in the TBM. They also suggest new research directions and may help users in selecting the most appropriate method for each particular application, depending on the nature of the information at hand.

This paper explains how multisensor data fusion and target identification can be performed within the transferable belief model (TBM), a model for the representation of quantified uncertainty based on belief functions. 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 present how this method applies in practice. We compare its solution with the classical one, illustrating it with an embarrassing example, where the TBM and the probability solutions completely disagree. Computational efficiency of the belief-function solution was supposedly proved in a study that we reproduce and we show that in fact the opposite conclusions hold. The results presented here can be extended directly to many problems of data fusion and diagnosis.

This paper presents a method for assessing the reliability of a sensor in a classification problem based on the transferable belief model. First, we develop a method for the evaluation of the reliability of a sensor when considered alone. The method is based on finding the discounting factor minimizing the distance between the pignistic probabilities computed from the discounted beliefs and the actual values of data. Next, we develop a method for assessing the reliability of several sensors that are supposed to work jointly and their readings are aggregated. The discounting factors are computed on the basis of minimizing the distance between the pignistic probabilities computed from the combined discounted belief functions and the actual values of data.

In the transferable belief model, a model for the quantified representation of beliefs, some masses can be allocated to the empty set. It reflects the conflict between the sources of information. This quantified conflict can be used in order to solve the problem of data association in a multi-target detection problem. We present and illustrate the procedure by studying an example based on the detection of submarines. Their number and the association of each sensor to a particular source are determined by the procedure. © 2001 John Wiley & Sons, Inc.

The problem of combining pieces of information issued from several sources can be encountered in various fields of application. This paper aims at presenting the different aspects of information fusion in different domains, such as databases, regulations, preferences, sensor fusion, etc., at a quite general level. We first present different types of information encountered in fusion problems, and different aims of the fusion process. Then we focus on representation issues which are relevant when discussing fusion problems. An important issue is then addressed, the handling of conflicting information. We briefly review different domains where fusion is involved, and describe how the fusion problems are stated in each domain. Since the term fusion can have different, more or less broad, meanings, we specify later some terminology with respect to related problems, that might be included in a broad meaning of fusion. Finally we briefly discuss the difficult aspects of validation and evaluation. © 2001 John Wiley & Sons, Inc.

The problem of assessing the value of a candidate is viewed here as a multiple combination problem. On the one hand, a candidate can be evaluated according to different criteria, and on the other hand, several experts are supposed to assess the value of candidates according to each criterion. Criteria are not equally important, experts are not equally competent or reliable. Moreover, levels of satisfaction of criteria, or levels of confidence are only assumed to take their values in linearly ordered scales, whose nature is rather qualitative. The problem is discussed within two frameworks, the transferable belief model (TBM) and the qualitative possibility theory (QPT). They respectively offer a quantitative and a qualitative setting for handling the problem, thus providing a way to emphasize what are the underlying assumptions in each approach. © 2001 John Wiley & Sons, Inc.

I give a short presentation of the most relevant elements of the transferable belief model and its use for problems related to the diagnostic process. These examples illustrate the use of the transferable belief model and, in particular, of the Generalized Bayesian Theorem. © 1998 John Wiley & Sons, Inc.13: 127–157, 1998

This paper advocates the use of nonpurely probabilistic approaches to higher-order uncertainty. One of the major arguments of Bayesian probability proponents is that representing uncertainty is always decision-driven and as a consequence, uncertainty should be represented by probability. Here we argue that representing partial ignorance is not always decision-driven. Other reasoning tasks such as belief revision for instance are more naturally carried out at the purely cognitive level. Conceiving knowledge representation and decision-making as separate concerns opens the way to nonpurely probabilistic representations of incomplete knowledge. It is pointed out that within a numerical framework, two numbers are needed to account for partial ignorance about events, because on top of truth and falsity, the state of total ignorance must be encoded independently of the number of underlying alternatives. The paper also points out that it is consistent to accept a Bayesian view of decision-making and a non-Bayesian view of knowledge representation because it is possible to map nonprobabilistic degrees of belief to betting probabilities when needed. Conditioning rules in non-Bayesian settings are reviewed, and the difference between focusing on a reference class and revising due to the arrival of new information is pointed out. A comparison of Bayesian and non-Bayesian revision modes is discussed on a classical example.

We present a decision support system which is based on the transferable belief model (TBM), a model to represent someone's degree of belief based on belief functions. The system performs reasoning and decision making by integrating a system for belief propagation and a system for Bayesian decision analysis. The two subsystems are developed within the framework of the valuation-based systems. They are connected through the pignistic transformation as described in the context of the TBM. The system takes as inputs the user's beliefs and utilities, and suggests either the optimal decision or the optimal sequence of decisions. An example concerning a nuclear waste disposal problem is given to demonstrate the applicability of the system in a real-world domain.

We present two methods to provide explanations for reasoning with belief functions. One approach, inspired by Strat's method, is based on sensitivity analysis, but its computation is simpler thus easier to implement than Strat's. The other approach is to examine the impact of each piece of evidence on the conclusion based on the measure of the information content provided by the evidence. We show the property of additivity for each pieces of evidence that are conditional independent within the context of the valuation-based systems. We give an example to show how these approaches are applied in an evidential network.

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Models based on belief functions have been often assimilated to models based on random sets. We show that this analogy does not resist when the conditioning process is considered.

A description of the transferable belief model, which is used to quantify degrees of belief based on belief functions, is given. The impact of open- and closed-world assumption on conditioning is discussed. The nature of the frame of discernment on which a degree of belief will be established is discussed. A set of axioms justifying Dempster's rule for the combination of belief functions induced by two distinct evidences is presented.>

Models for fuzzy deductive reasoning are becoming important in the field of knowledge-based systems. Zadeh suggested a compositional rule of inference, also called Generalized Modus Ponens. In order to study the fine structure of this model, we test seven rules of implication, usually found in the fuzzy literature, and two kinds of compositional rule with several properties which seems to be required by commonsense reasoning. But, as no rule is shown to satisfy these properties, we propose a new model for fuzzy Modus Ponens. the main idea of this model is to find a fuzzy extension of the meta-level rule of inference, in comparison with the object-level extension of the disjunctive syllogism such as the Zadeh's model. It is shown that our model satisfies all the intuitively required properties, and moreover is computationally very easy to apply.