Frédéric Pichon

Relevance and truthfulness in information correction and fusion

A general approach to information correction and fusion for belief functions is proposed, where not only may the information items be irrelevant, but sources may lie as well. We introduce a new correction scheme, which takes into account uncertain metaknowledge on the sources relevance and truthfulness and that generalizes Shafers discounting operation. We then show how to reinterpret all connectives of Boolean logic in terms of source behavior assumptions with respect to relevance and truthfulness. We are led to generalize the unnormalized Dempsters rule to all Boolean connectives, while taking into account the uncertainties pertaining to assumptions concerning the behavior of sources. Eventually, we further extend this approach to an even more general setting, where source behavior assumptions do not have to be restricted to relevance and truthfulness. We also establish the commutativity property between correction and fusion processes, when the behaviors of the sources are independent.

The Unnormalized Dempster’s Rule of Combination: A New Justification from the Least Commitment Principle and Some Extensions

In the Transferable Belief Model, belief functions are usually combined using the unnormalized Dempster’s rule (also called the TBM conjunctive rule). This rule is used because of its intuitive appeal and because it has received formal justifications as opposed to the many other rules of combination that have been proposed in the literature. This article confirms the singularity of the TBM conjunctive rule by presenting a new formal justification based on (1) the canonical decomposition of belief functions, (2) the least commitment principle and (3) the requirement of having the vacuous belief function as neutral element of the combination. A similar result is also presented for the TBM disjunctive rule. Eventually, the existence of infinite families of rules having similar properties as those two rules is pointed out.

A Consistency-Specificity Trade-Off to Select Source Behavior in Information Fusion

Combining pieces of information provided by several sources without or with little prior knowledge about the behavior of the sources is an old yet still important and rather open problem in the belief function theory. In this paper, we propose an approach to select the behavior of sources based on a very general and expressive fusion scheme, that has the important advantage of making clear the assumptions made about the sources. The selection process itself relies on two cornerstones that are the notions of specificity and consistency of a knowledge representation, and that we adapt to the considered fusion scheme. We illustrate our proposal on different examples and show that the proposed approach actually encompasses some important existing fusion strategies.

Proposition of a semi-automatic possibilistic information scoring process

This paper proposes a semi-automatic three step information scoring process that starts from constructs representing structured pieces of information and a user query. It first identifies the constructs relevant to answer the user question, based on their similarity to the query. The relevant items are then individually scored, taking into account both the reliability of their source and the certainty the latter expresses through its choice of linguistic terms. Lastly, these individual scores are fused, modeling a corroboration process that takes into account information obsolescence and source relations. This procedure is performed in the framework of possibility theory, relying on the definition of the appropriate aggregation operators.

On the α-Conjunctions for Combining Belief Functions

The α-conjunctions basically represent the set of associative, commutative and linear operators for belief functions with the vacuous belief function as neutral element. Besides, they include as particular case the unnormalized Dempster’s rule. They are thus particularly interesting from a formal standpoint. However, they suffer from a main limitation: they lack a clear interpretation in general. In this paper, an interpretation for these combination rules is proposed, based on a new framework that allows the integration of meta-knowledge on the various forms of lack of truthfulness of the information sources.

T-norm and uninorm-based combination of belief functions

The distinctness assumption is a limitation to the use of the unnormalized Dempsters rule. Denoeux recently proposed an alternative rule, called the cautious rule, which does not rely on this assumption. He further showed that the cautious rule and the unnormalized Dempsters rule belong to two families of combination rules having different algebraic properties. This paper revisits this latter point: the cautious and unnormalized Dempsters rules can be seen as member of families of combination rules based on triangular norms and uninorms, respectively. Furthermore, both rules have a special position in their respective family: they are the least committed elements. This paper also provides a means of obtaining an infinity of rules in the family of uninorm-based combination rules.

On Latent Belief Structures

Based on the canonical decomposition of belief functions, Smets introduced the concept of a latent belief structure (LBS). This concept is revisited in this article. The study of the combination of LBSs allows us to propose a less committed version of Dempsters rule, resulting in a commutative, associative and idempotent rule of combination for LBSs. This latter property makes it suitable to combine non distinct bodies of evidence. A sound method based on the plausibility transformation is also given to infer decisions from LBSs. In addition, an extension of the new rule is proposed so that it may be used to optimize the combination of imperfect information with respect to the decisions inferred.

Evidential Joint Calibration of Binary SVM Classifiers Using Logistic Regression

In a context of multiple classifiers, a calibration step based on logistic regression is usually used to independently transform each classifier output into a probability distribution, to be then able to combine them. This calibration has been recently refined, using the evidence theory, to better handle uncertainties. In this paper, we propose to use this logistic-based calibration in a multivariable scenario, i.e., to consider jointly all the outputs returned by the classifiers, and to extend this approach to the evidential framework. Our evidential approach was tested on generated and real datasets and presents several advantages over the probabilistic version.

The Capacitated Vehicle Routing Problem with Evidential Demands: A Belief-Constrained Programming Approach

This paper studies a vehicle routing problem, where vehicles have a limited capacity and customer demands are uncertain and represented by belief functions. More specifically, this problem is formalized using a belief function based extension of the chance-constrained programming approach, which is a classical modeling of stochastic mathematical programs. In addition, it is shown how the optimal solution cost is influenced by some important parameters involved in the model. Finally, some instances of this difficult problem are solved using a simulated annealing metaheuristic, demonstrating the feasibility of the approach.

Truthfulness in Contextual Information Correction

Recently, a dual reinforcement process to contextual discounting was introduced. However, it lacked a clear interpretation. In this paper, we propose a new perspective on contextual discounting: it can be seen as successive corrections corresponding to simple contextual lies. Most interestingly, a similar interpretation is provided for the reinforcement process. Two new contextual correction mechanisms, which are similar yet complementary to the two existing ones, are also introduced.