Evidence Theory (a.k.a. Dempster-Shafer theory) offers a quite general and powerful setting to reason under uncertainty. However, most of the approaches allowing one to instantiate mass functions, the basic building block of the theory, rely on measured, objective data, and there are very few approaches to instantiate them from subjective, expert opinions. Here we suggest a viable solution, based on the concept of pairwise comparisons, for the elicitation of such subjective information. The approach is based on the well-established body of knowledge on the theory of pairwise comparisons and shows its flexibility as it can incorporate multiple representations for the subjective judgments and multiple experts, just to cite two possible extensions.

One way to make decisions under uncertainty is to select an optimal option from a possible range of options, by maximizing the expected utilities derived from a probability model. However, under severe uncertainty, identifying precise probabilities is hard. For this reason, imprecise probability models uncertainty through convex sets of probabilities, and considers decision rules that can return multiple options to reflect insufficient information. Many well-founded decision rules have been studied in the past, but none of those standard rules are able to control the number of returned alternatives. This can be a problem for large decision problems, due to the cognitive burden decision makers have to face when presented with a large number of alternatives. Our contribution proposes regret-based ideas to construct new decision rules which return a bounded number of options, where the limit on the number of options is set in advance by the decision maker as an expression of their cognitive limitation. We also study their consistency and numerical behaviour.

We explore the relationship between possibility measures (supremum preserving normed measures) and p-boxes (pairs of cumulative distribution functions) on totally preordered spaces, extending earlier work in this direction by De Cooman and Aeyels, among others. We start by demonstrating that only those p-boxes who have 0–1-valued lower or upper cumulative distribution function can be possibility measures, and we derive expressions for their natural extension in this case. Next, we establish necessary and sufficient conditions for a p-box to be a possibility measure. Finally, we show that almost every possibility measure can be modelled by a p-box, simply by ordering elements by increasing possibility. Whence, any techniques for p-boxes can be readily applied to possibility measures. We demonstrate this by deriving joint possibility measures from marginals, under varying assumptions of independence, using a technique known for p-boxes. Doing so, we arrive at a new rule of combination for possibility measures, for the independent case.

There are many available methods to integrate information source reliability in an uncertainty representation, but there are only a few works focusing on the problem of evaluating this reliability. However, data reliability and confidence are essential components of a data warehousing system, as they influence subsequent retrieval and analysis. In this paper, we propose a generic method to assess data reliability from a set of criteria using the theory of belief functions. Customizable criteria and insightful decisions are provided. The chosen illustrative example comes from real-world data issued from the Sym'Previus predictive microbiology oriented data warehouse.

Information is said to be bipolar when it has a positive and a negative part. The problem of representing and processing such bipolar information has recently received a lot of attention in uncertainty theories. In this paper, we are concerned with the representation of asymmetric bipolarity, i.e., with situations where positive and negative information are unrelated and processed in parallel. In this latter case, positive information consists of observations of experiment results, showing what values are possible, whereas negative information consists of constraints (e.g., provided by an expert), restricting the range of possible variable values. Up to now, there are no proposition as to how such bipolar information can be treated in the framework of imprecise probability theory, i.e., when information is represented by convex sets of probabilities. In this paper, we propose the basis of such a framework and provide some illustrative examples. © 2011 Wiley Periodicals, Inc.