The Basic Principles of Uncertain Information Fusion. An organized review of merging rules in different representation frameworks

We propose and advocate basic principles for the fusion of incomplete or uncertain information items, that should apply regardless of the formalism adopted for representing pieces of information coming from several sources. This formalism can be based on sets, logic, partial orders, possibility theory, belief functions or imprecise probabilities. We propose a general notion of information item representing incomplete or uncertain information about the values of an entity of interest. It is supposed to rank such values in terms of relative plausibility, and explicitly point out impossible values. Basic issues affecting the results of the fusion process, such as relative information content and consistency of information items, as well as their mutual consistency, are discussed. For each representation setting, we present fusion rules that obey our principles, and compare them to postulates specific to the representation proposed in the past. In the crudest (Boolean) representation setting (using a set of possible values), we show that the understanding of the set in terms of most plausible values, or in terms of non-impossible ones matters for choosing a relevant fusion rule. Especially, in the latter case our principles justify the method of maximal consistent subsets, while the former is related to the fusion of logical bases. Then we consider several formal settings for incomplete or uncertain information items, where our postulates are instantiated: plausibility orderings, qualitative and quantitative possibility distributions, belief functions and convex sets of probabilities. The aim of this paper is to provide a unified picture of fusion rules across various uncertainty representation settings

Belief Change in Reasoning Agents: Axiomatizations, Semantics and Computations

The capability of changing beliefs upon new information in a rational and efficient way is crucial for an intelligent agent. Belief change therefore is one of the central research fields in Artificial Intelligence (AI) for over two decades. In the AI literature, two different kinds of belief change operations have been intensively investigated: belief update, which deal with situations where the new information describes changes of the world; and belief revision, which assumes the world is static. As another important research area in AI, reasoning about actions mainly studies the problem of representing and reasoning about effects of actions. These two research fields are closely related and apply a common underlying principle, that is, an agent should change its beliefs (knowledge) as little as possible whenever an adjustment is necessary. This lays down the possibility of reusing the ideas and results of one field in the other, and vice verse. This thesis aims to develop a general framework and devise computational models that are applicable in reasoning about actions. Firstly, I shall propose a new framework for iterated belief revision by introducing a new postulate to the existing AGM/DP postulates, which provides general criteria for the design of iterated revision operators. Secondly, based on the new framework, a concrete iterated revision operator is devised. The semantic model of the operator gives nice intuitions and helps to show its satisfiability of desirable postulates. I also show that the computational model of the operator is almost optimal in time and space-complexity. In order to deal with the belief change problem in multi-agent systems, I introduce a concept of mutual belief revision which is concerned with information exchange among agents. A concrete mutual revision operator is devised by generalizing the iterated revision operator. Likewise, a semantic model is used to show the intuition and many nice properties of the mutual revision operator, and the complexity of its computational model is formally analyzed. Finally, I present a belief update operator, which takes into account two important problems of reasoning about action, i.e., disjunctive updates and domain constraints. Again, the updated operator is presented with both a semantic model and a computational model

New Graphical Model for Computing Optimistic Decisions in Possibility Theory Framework

This paper first proposes a new graphical model for decision making under uncertainty based on min-based possibilistic networks. A decision problem under uncertainty is described by means of two distinct min-based possibilistic networks: the first one expresses agent's knowledge while the second one encodes agent's preferences representing a qualitative utility. We then propose an efficient algorithm for computing optimistic optimal decisions using our new model for representing possibilistic decision making under uncertainty. We show that the computation of optimal decisions comes down to compute a normalization degree of the junction tree associated with the graph resulting from the fusion of agent's beliefs and preferences. This paper also proposes an alternative way for computing optimal optimistic decisions. The idea is to transform the two possibilistic networks into two equivalent possibilistic logic knowledge bases, one representing agent's knowledge and the other represents agent's preferences. We show that computing an optimal optimistic decision comes down to compute the inconsistency degree of the union of the two possibilistic bases augmented with a given decision

An Analysis of Sum-Based Incommensurable Belief Base Merging

International audienceDifferent methods have been proposed for merging multiple and potentially conflicting informations. Sum-based operators offer a natural method for merging commensurable prioritized belief bases. Their popularity is due to the fact that they satisfy the majority property and they adopt a non cautious attitude in deriving plausible conclusions. This paper analyses the sum-based merging operator when sources to merge are incommensurable, namely they do not share the same meaning of uncertainty scales. We first show that the obtained merging operator can be equivalently characterized either in terms of an infinite set of compatible scales, or by a well-known Pareto ordering on a set of models. We then study different families of compatible scales useful for merging process. This paper also provides a postulates-based analysis of our merging operators

The logical encoding of Sugeno integrals

International audienceSugeno integrals are a well-known family of qualitative multiple criteria aggregation operators. The paper investigates how the behavior of these operators can be described in a prioritized propositional logic language, namely possibilistic logic. The case of binary-valued criteria, which amounts to providing a logical description of the fuzzy measure underlying the integral, is first considered. The general case of a Sugeno integral when criteria are valued on a discrete scale is then studied