Contradiction measures and specificity degrees of basic belief assignments

In the theory of belief functions, many measures of uncertainty have been introduced. However, it is not always easy to understand what these measures really try to represent. In this paper, we re-interpret some measures of uncertainty in the theory of belief functions. We present some interests and drawbacks of the existing measures. On these observations, we introduce a measure of contradiction. Therefore, we present some degrees of non-specificity and Bayesianity of a mass. We propose a degree of specificity based on the distance between a mass and its most specific associated mass. We also show how to use the degree of specificity to measure the specificity of a fusion rule. Illustrations on simple examples are given.

General combination rules for qualitative and quantitative beliefs

Martin and Osswald \cite{Martin07} have recently proposed many generalizations of combination rules on quantitative beliefs in order to manage the conflict and to consider the specificity of the responses of the experts. Since the experts express themselves usually in natural language with linguistic labels, Smarandache and Dezert \cite{Li07} have introduced a mathematical framework for dealing directly also with qualitative beliefs. In this paper we recall some element of our previous works and propose the new combination rules, developed for the fusion of both qualitative or quantitative beliefs.

Generalized proportional conflict redistribution rule applied to Sonar imagery and Radar targets classification

In this chapter, we present two applications in information fusion in order to evaluate the generalized proportional conflict redistribution rule presented in the chapter \cite{Martin06a}. Most of the time the combination rules are evaluated only on simple examples. We study here different combination rules and compare them in terms of decision on real data. Indeed, in real applications, we need a reliable decision and it is the final results that matter. Two applications are presented here: a fusion of human experts opinions on the kind of underwater sediments depict on sonar image and a classifier fusion for radar targets recognition.

Experts Fusion and Multilayer Perceptron Based on Belief Learning for Sonar Image Classification

The sonar images provide a rapid view of the seabed in order to characterize it. However, in such as uncertain environment, real seabed is unknown and the only information we can obtain, is the interpretation of different human experts, sometimes in conflict. In this paper, we propose to manage this conflict in order to provide a robust reality for the learning step of classification algorithms. The classification is conducted by a multilayer perceptron, taking into account the uncertainty of the reality in the learning stage. The results of this seabed characterization are presented on real sonar images.

Une nouvelle règle de combinaison répartissant le conflit - Applications en imagerie Sonar et classification de cibles Radar

These last years, there were many studies on the problem of the conflict coming from information combination, especially in evidence theory. We can summarise the solutions for manage the conflict into three different approaches: first, we can try to suppress or reduce the conflict before the combination step, secondly, we can manage the conflict in order to give no influence of the conflict in the combination step, and then take into account the conflict in the decision step, thirdly, we can take into account the conflict in the combination step. The first approach is certainly the better, but not always feasible. It is difficult to say which approach is the best between the second and the third. However, the most important is the produced results in applications. We propose here a new combination rule that distributes the conflict proportionally on the element given this conflict. We compare these different combination rules on real data in Sonar imagery and Radar target classification.

Human expert fusion for image classification

In image classification, merging the opinion of several human experts is very important for different tasks such as the evaluation or the training. Indeed, the ground truth is rarely known before the scene imaging. We propose here different models in order to fuse the informations given by two or more experts. The considered unit for the classification, a small tile of the image, can contain one or more kind of the considered classes given by the experts. A second problem that we have to take into account, is the amount of certainty of the expert has for each pixel of the tile. In order to solve these problems we define five models in the context of the Dempster-Shafer Theory and in the context of the Dezert-Smarandache Theory and we study the possible decisions with these models.

A new generalization of the proportional conflict redistribution rule stable in terms of decision

In this chapter, we present and discuss a new generalized proportional conflict redistribution rule. The Dezert-Smarandache extension of the Demster-Shafer theory has relaunched the studies on the combination rules especially for the management of the conflict. Many combination rules have been proposed in the last few years. We study here different combination rules and compare them in terms of decision on didactic example and on generated data. Indeed, in real applications, we need a reliable decision and it is the final results that matter. This chapter shows that a fine proportional conflict redistribution rule must be preferred for the combination in the belief function theory.

Toward a combination rule to deal with partial conflict and specificity in belief functions theory

We present and discuss a mixed conjunctive and disjunctive rule, a generalization of conflict repartition rules, and a combination of these two rules. In the belief functions theory one of the major problem is the conflict repartition enlightened by the famous Zadeh's example. To date, many combination rules have been proposed in order to solve a solution to this problem. Moreover, it can be important to consider the specificity of the responses of the experts. Since few year some unification rules are proposed. We have shown in our previous works the interest of the proportional conflict redistribution rule. We propose here a mixed combination rule following the proportional conflict redistribution rule modified by a discounting procedure. This rule generalizes many combination rules.