Our aim in this paper is to clarify the notion of independence for imprecise probabilities. Suppose that two marginal experiments are each described by an imprecise probability model, i.e., by a convex set of probability distributions or an equivalent model such as upper and lower probabilities or previsions. Then there are several ways to define independence of the two experiments and to construct an imprecise probability model for the joint experiment. We survey and compare six definitions of independence. To clarify the meaning of the definitions and the relationships between them, we give simple examples which involve drawing balls from urns. For each concept of independence, we give a mathematical definition, an intuitive or behavioural interpretation, assumptions under which the definition is justified, and an example of an urn model to which the definition is applicable. Each of the independence concepts we study appears to be useful in some kinds of application. The concepts of strong independence and epistemic independence appear to be the most frequently applicable.

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.

This paper considers two measures of entropy for the Theory of Evidence and studies their properties. The first measure is based on the measures of entropy and specificity as defined by Yager. The other one may easily be applied to more general classes of fuzzy measures.

Directed graphic models based on conditional independence provide a compact and concise representation of an expert's subjective belief about existing relationships between variables. Faced with the task of building a greater model, each expert must be a specialist in some subset of the whole knowledge domain. It would be desirable to aggregate the knowledge provided by those specialists under the form of graphical models into a single and more general representation. This article studies the consensus model that would be obtained by combining two graphs associated with Bayesian networks and applying the union and intersection of their independencies.