Sur la décombinaison de fonctions de croyance

International audienceThe evidence combination is a kind of decision-level information fusion in the theory of belief functions. Given two basic belief assignments (BBAs) originated from different sources, one can combine them using some combination rule, e.g., Dempster's rule to expect a better decision result. If one only has a combined BBA, how to determine the original two BBAs to combine? This can be considered as a defusion of information. This is useful, e.g., one can analyze the difference or dissimilarity between two different information sources based on the BBAs obtained using evidence decombination. Therefore, in this paper, we research on such a defusion in the theory of belief functions. We find that it is a well-posed problem if one original BBA and the combined BBA are both available, and it is an under-determined problem if both BBAs to combine are unknown. We propose an optimization-based approach for the evidence decombination according to the criteria of divergence maximization. Numerical examples are provided illustrate and verify our proposed decombination approach, which is expected to be used in applications such the difference analysis between information sources in information fusion systems when the original BBAs are discarded, and performance evaluation of combination rules

ARTIFICIAL INTELLIGENCE DIALECTS OF THE BAYESIAN BELIEF REVISION LANGUAGE

Rule-based expert systems must deal with uncertain data, subjective expert opinions, and inaccurate decision rules. Computer scientists and psychologists have proposed and implemented a number of belief languages widely used in applied systems, and their normative validity is clearly an important question, both on practical as well on theoretical grounds. Several well-know belief languages are reviewed, and both previous work and new insights into their Bayesian interpretations are presented. In particular, the authors focus on three alternative belief-update models the certainty factors calculus, Dempster-Shafer simple support functions, and the descriptive contrast/inertia model. Important "dialectsâ of these languages are shown to be isomorphic to each other and to a special case of Bayesian inference. Parts of this analysis were carried out by other authors; these results were extended and consolidated using an analytic technique designed to study the kinship of belief languages in general.Information Systems Working Papers Serie

Hybridization of Bayesian networks and belief functions to assess risk. Application to aircraft deconstruction

This paper aims to present a study on knowledge management for the disassembly of end-of-life aircraft. We propose a model using Bayesian networks to assess risk and present three approaches to integrate the belief functions standing for the representation of fuzzy and uncertain knowledge

Restricted Value Iteration: Theory and Algorithms

Value iteration is a popular algorithm for finding near optimal policies for POMDPs. It is inefficient due to the need to account for the entire belief space, which necessitates the solution of large numbers of linear programs. In this paper, we study value iteration restricted to belief subsets. We show that, together with properly chosen belief subsets, restricted value iteration yields near-optimal policies and we give a condition for determining whether a given belief subset would bring about savings in space and time. We also apply restricted value iteration to two interesting classes of POMDPs, namely informative POMDPs and near-discernible POMDPs

The belief noisy-or model applied to network reliability analysis

One difficulty faced in knowledge engineering for Bayesian Network (BN) is the quan-tification step where the Conditional Probability Tables (CPTs) are determined. The number of parameters included in CPTs increases exponentially with the number of parent variables. The most common solution is the application of the so-called canonical gates. The Noisy-OR (NOR) gate, which takes advantage of the independence of causal interactions, provides a logarithmic reduction of the number of parameters required to specify a CPT. In this paper, an extension of NOR model based on the theory of belief functions, named Belief Noisy-OR (BNOR), is proposed. BNOR is capable of dealing with both aleatory and epistemic uncertainty of the network. Compared with NOR, more rich information which is of great value for making decisions can be got when the available knowledge is uncertain. Specially, when there is no epistemic uncertainty, BNOR degrades into NOR. Additionally, different structures of BNOR are presented in this paper in order to meet various needs of engineers. The application of BNOR model on the reliability evaluation problem of networked systems demonstrates its effectiveness