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

The Correlation Problem in Sensor Fusion in a Possibilistic Framework

International audienceThis paper addresses the correlation problem which is central in sensor fusion, from the viewpoint of possibility theory. This problem aims at separating pieces of information pertaining to different objects and to gather those which are likely to pertain to the same object. We present two different views of the problem, one based on similarity relations, while the other discusses the problem in a logical framework

Idempotent conjunctive combination of belief functions: Extending the minimum rule of possibility theory.

IATE : Axe 5 Application intégrée de la connaissance, de l’information et des technologies permettant d’accroître la qualité et la sécurité des aliments Contact : [email protected] (S. Destercke), [email protected] (D. Dubois) Fax: +33 0 4 9961 3076.International audienceWhen conjunctively merging two belief functions concerning a single variable but coming from different sources, Dempster rule of combination is justified only when information sources can be considered as independent. When dependencies between sources are ill-known, it is usual to require the property of idempotence for the merging of belief functions, as this property captures the possible redundancy of dependent sources. To study idempotent merging, different strategies can be followed. One strategy is to rely on idempotent rules used in either more general or more specific frameworks and to study, respectively, their particularisation or extension to belief functions. In this paper, we study the feasibility of extending the idempotent fusion rule of possibility theory (the minimum) to belief functions. We first investigate how comparisons of information content, in the form of inclusion and least-commitment, can be exploited to relate idempotent merging in possibility theory to evidence theory. We reach the conclusion that unless we accept the idea that the result of the fusion process can be a family of belief functions, such an extension is not always possible. As handling such families seems impractical, we then turn our attention to a more quantitative criterion and consider those combinations that maximise the expected cardinality of the joint belief functions, among the least committed ones, taking advantage of the fact that the expected cardinality of a belief function only depends on its contour function

Toward a General Framework for Information Fusion

National audienceDepending on the representation setting, different combination rules have been proposed for fusing information from distinct sources. Moreover in each setting, different sets of axioms that combination rules should satisfy have been advocated, thus justifying the existence of alternative rules (usually motivated by situations where the behavior of other rules was found unsatisfactory). These sets of axioms are usually purely considered in their own settings, without in-depth analysis of common properties essential for all the settings. This paper introduces core properties that, once properly instantiated, are meaningful in different representation settings ranging from logic to imprecise probabilities. The following representation settings are especially considered: classical set representation, possibility theory, and evidence theory, the latter encompassing the two other ones as special cases. This unified discussion of combination rules across different settings is expected to provide a fresh look on some old but basic issues in information fusion

Data fusion in image processing: information models and decisions

We present the definitions and necessary steps for data fusion in image processing . We introduce then the different tools used for modelizing information issued from various sensors, for combining these pieces of information, and then for taking a decision . We focus on probabilistic and Bayesian inference, evidence theory, fuzzy sets and possibility theory. We underline the key features of data fusion in image processing : uncertainty and imprecision . We show how the management of these two characteristics, intrinsic to image processing, induces choices of models and fusion operators.Nous présentons les définitions et les étapes nécessaires à la fusion de données en traitement des images. Nous introduisons ensuite les divers outils utilisés à ce jour pour modéliser les informations issues de divers capteurs, combiner ces informations puis décider, en nous focalisant sur les théories probabilistes et bayésiennes, des croyances, des ensembles flous et des possibilités. Nous insistons sur les points centraux de la fusion d'images: l'incertain et l'imprécis. Nous montrons comment la prise en compte de ces deux caractéristiques intrinsèques du traitement de l'image induit des choix dans les modèles et les opérateurs de fusio

Applying new uncertainty related theories and multicriteria decision analysis methods to snow avalanche risk management

International audienceMaking the best decision in the event of a snow avalanche encounters problems in the assessment and management process because of the lack of information and knowledge on natural phenomena and the heterogeneity and reliability of the information sources available (historical data, field measurements, and expert assessments). One major goal today is therefore to aid decision making by improving the quality, quantity, and reliability of the available information. This article presents a new method called evidential reasoning and multicriteria decision analysis (ER-MCDA) to help decision making by considering information imperfections arising from several more or less reliable and possibly conflicting sources of information. First, the principles of the existing methods are reviewed. Classical methods of multicriteria decision making and existing theories attempting to represent and propagate information imperfections are described. In a second point, we describe the principle of the ER-MCDA method combining multicriteria decision analysis (MCDA) to model the decision-making process and fuzzy sets theory, possibility theory, and evidence theory to represent, fuse and propagate information imperfections. Experts, considered more or less reliable, provide imprecise and uncertain evaluations of quantitative and qualitative criteria that are combined through information fusion. The method is applied to a simplified version of an existing system aiming to evaluate the sensitivity of avalanche sites. This new method makes it possible to consider both the importance of the information available and reliability in the decision process. It also contributes to improving traceability. Other developments designed to handle other assessment problems such as avalanche triggering conditions or data quality are in progress

A fuzzy diagnosis of multi-fault state based on information fusion from multiple sensors

This paper presents a fuzzy diagnosis for detecting and distinguishing multi-fault state, the method is constructed on the basis of possibility theory and support vector machines (SVMs) with information fusion from multiple sensors. Non-dimensional symptom parameters (NSPs) are defined to reflect the characteristics of vibration information, and principal component analysis (PCA) is used to evaluate and select sensitive NSPs of each sensor. SVMs are employed to fuse vibration information from different sensors into an effective synthetic symptom parameter (SSP) for increasing diagnostic sensitivity, then the possibility function of the SSP is used to construct a fuzzy diagnosis for fault detection and fault-type identification by possibility theory. Practical examples of diagnosis for a roller bearing used in a test bench are given to show that multi-fault states of bearing can be identified precisely by the proposed method

Robust Multi-Sensor Multi-Target Tracking Using Possibility Labeled Multi-Bernoulli Filter

With the increasing complexity of multiple target tracking scenes, a single sensor may not be able to effectively monitor a large number of targets. Therefore, it is imperative to extend the single-sensor technique to Multi-Sensor Multi-Target Tracking (MSMTT) for enhanced functionality. Typical MSMTT methods presume complete randomness of all uncertain components, and therefore effective solutions such as the random finite set filter and covariance intersection method have been derived to conduct the MSMTT task. However, the presence of epistemic uncertainty, arising from incomplete information, is often disregarded within the context of MSMTT. This paper develops an innovative possibility Labeled Multi-Bernoulli (LMB) Filter based on the labeled Uncertain Finite Set (UFS) theory. The LMB filter inherits the high robustness of the possibility generalized labeled multi-Bernoulli filter with simplified computational complexity. The fusion of LMB UFSs is derived and adapted to develop a robust MSMTT scheme. Simulation results corroborate the superior performance exhibited by the proposed approach in comparison to typical probabilistic methods

A two-step fusion process for multi-criteria decision applied to natural hazards in mountains

Mountain river torrents and snow avalanches generate human and material damages with dramatic consequences. Knowledge about natural phenomenona is often lacking and expertise is required for decision and risk management purposes using multi-disciplinary quantitative or qualitative approaches. Expertise is considered as a decision process based on imperfect information coming from more or less reliable and conflicting sources. A methodology mixing the Analytic Hierarchy Process (AHP), a multi-criteria aid-decision method, and information fusion using Belief Function Theory is described. Fuzzy Sets and Possibilities theories allow to transform quantitative and qualitative criteria into a common frame of discernment for decision in Dempster-Shafer Theory (DST ) and Dezert-Smarandache Theory (DSmT) contexts. Main issues consist in basic belief assignments elicitation, conflict identification and management, fusion rule choices, results validation but also in specific needs to make a difference between importance and reliability and uncertainty in the fusion process