Contradiction measures and specificity degrees of basic belief assignments

In the theory of belief functions, many measures of uncertainty have been introduced. However, it is not always easy to understand what these measures really try to represent. In this paper, we re-interpret some measures of uncertainty in the theory of belief functions. We present some interests and drawbacks of the existing measures. On these observations, we introduce a measure of contradiction. Therefore, we present some degrees of non-specificity and Bayesianity of a mass. We propose a degree of specificity based on the distance between a mass and its most specific associated mass. We also show how to use the degree of specificity to measure the specificity of a fusion rule. Illustrations on simple examples are given

Weighted Evidence Combination Rule Based on Evidence Distance and Uncertainty Measure: An Application in Fault Diagnosis

Conflict management in Dempster-Shafer theory (D-S theory) is a hot topic in information fusion. In this paper, a novel weighted evidence combination rule based on evidence distance and uncertainty measure is proposed. The proposed approach consists of two steps. First, the weight is determined based on the evidence distance. Then, the weight value obtained in first step is modified by taking advantage of uncertainty. Our proposed method can efficiently handle high conflicting evidences with better performance of convergence. A numerical example and an application based on sensor fusion in fault diagnosis are given to demonstrate the efficiency of our proposed method

Algorithmes Forward-Backward et décodage de Viterbi dans le cadre du Modèle des Croyances Transférables : Application à la classification de séquences vidéos

Nous présentons une version crédibiliste des Modèles de Markov Cachés, particulièrement les procédures « forward », « backward » et « Viterbi » définies dans le cadre du Modèle des Croyances Transférables de Smets. La reformulation est basée sur le Théorème de Bayes Généralisé ainsi que sur les travaux de Smets sur les Réseaux Evidentiels. Un critère basé sur le conflit est aussi proposé pour inférer des séquences. Les algorithmes proposés sont testés sur des vidéos d'athlétisme

Multi-ROI Association and Tracking With Belief Functions: Application to Traffic Sign Recognition

This paper presents an object tracking algorithm using belief functions applied to vision-based traffic sign recognition systems. This algorithm tracks detected sign candidates over time in order to reduce false positives due to data fusion formalization. In the first stage, regions of interest (ROIs) are detected and combined using the transferable belief model semantics. In the second stage, the local pignistic probability algorithm generates the associations maximizing the belief of each pairing between detected ROIs and ROIs tracked by multiple Kalman filters. Finally, the tracks are analyzed to detect false positives. Due to a feedback loop between the multi-ROI tracker and the ROI detector, the solution proposed reduces false positives by up to 45%, whereas computation time remains very low

Advances and Applications of Dezert-Smarandache Theory (DSmT) for Information Fusion (Collected Works), Vol. 4

The fourth volume on Advances and Applications of Dezert-Smarandache Theory (DSmT) for information fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics. The contributions (see List of Articles published in this book, at the end of the volume) have been published or presented after disseminating the third volume (2009, http://fs.unm.edu/DSmT-book3.pdf) in international conferences, seminars, workshops and journals. First Part of this book presents the theoretical advancement of DSmT, dealing with Belief functions, conditioning and deconditioning, Analytic Hierarchy Process, Decision Making, Multi-Criteria, evidence theory, combination rule, evidence distance, conflicting belief, sources of evidences with different importance and reliabilities, importance of sources, pignistic probability transformation, Qualitative reasoning under uncertainty, Imprecise belief structures, 2-Tuple linguistic label, Electre Tri Method, hierarchical proportional redistribution, basic belief assignment, subjective probability measure, Smarandache codification, neutrosophic logic, Evidence theory, outranking methods, Dempster-Shafer Theory, Bayes fusion rule, frequentist probability, mean square error, controlling factor, optimal assignment solution, data association, Transferable Belief Model, and others. More applications of DSmT have emerged in the past years since the apparition of the third book of DSmT 2009. Subsequently, the second part of this volume is about applications of DSmT in correlation with Electronic Support Measures, belief function, sensor networks, Ground Moving Target and Multiple target tracking, Vehicle-Born Improvised Explosive Device, Belief Interacting Multiple Model filter, seismic and acoustic sensor, Support Vector Machines, Alarm classification, ability of human visual system, Uncertainty Representation and Reasoning Evaluation Framework, Threat Assessment, Handwritten Signature Verification, Automatic Aircraft Recognition, Dynamic Data-Driven Application System, adjustment of secure communication trust analysis, and so on. Finally, the third part presents a List of References related with DSmT published or presented along the years since its inception in 2004, chronologically ordered

Vers le suivi d’objets dans un cadre évidentiel : représentation, filtrage dynamique et association

Intelligent systems are more and more present in our society, like the systems of surveillance and civilian or military sites protection. Their purpose is to detect intruders and present the alarms or threats to a distant operator. In our work, we are interested in such systems with the aim to better handle the quality of information presented to the operator in terms of reliability and precision. We focus on the image modality and we have to handle detections that are both uncertain and imprecise in order to present reliable objects to the operator.To specify our problem, we consider the following constraints. The first one is that the system is modular; one subpart of the system is the detection of fragments corresponding potentially to objects. Our second constraint is then to use only information derived from the geometry of these fragmentary detections: spatial location in the image and size of the detections. Then, a threat is supposed all the more important as the detections have an important size and are temporally persistent.The chosen formal framework is the belief functions theory that allows modeling imprecise and uncertain data. The contributions of this thesis deal with the objects representation in terms of imprecise and uncertain location of the objects and object filtering.The pertinent representation of information is a key point for estimation problems and decision making. A representation is good when simple and efficient criteria for the resolution of sub problems can be derived. The representation proposed has allowed us to derive, in a simple and rigorous way, an association criterion between new detections (fragments) and objects under construction. We remind that this association is a key step for several problems with unlabelled data that extends our contribution beyond of the considered application.Data filtering is used in many methods and algorithms to robustify the results using the expected data redundancy versus the noise inconsistency. Then, we formulated our problem in terms of dynamic estimation of a discernment frame including the 'true hypotheses'. This frame is dynamically estimated taking into account the new data (or observations) that allow us to detect two main types of errors, namely the duplication of some hypotheses (objects in our application) and the presence of false alarms (due to noise or false detections in our case).Finally, we show the possibility of coupling our sub-functions dealing with object construction and their filtering with a tracking process using higher level information such as classical tracking algorithm in image processing.Keywords: belief functions theory, data association, filtering.Les systèmes intelligents sont de plus en plus présents dans notre société à l’instar des systèmes de surveillance et de protection de sites civils ou militaires. Leur but est de détecter les intrus et remonter une alarme ou une menace à un opérateur distant. Dans nos travaux, nous nous intéressons à de tels systèmes avec comme objectif de gérer au mieux la qualité de l’information présentée à l’opérateur en termes de fiabilité et précision. Nous nous concentrons sur la modalité image en vue de gérer des détections à la fois incertaines et imprécises de façon à présenter des objets fiables à l’opérateur.Pour préciser notre problème nous posons les contraintes suivantes. La première est que le système soit modulaire, l’une des briques (ou sous-fonctions) du système étant la détection de fragments correspondant potentiellement à des objets. Notre deuxième contrainte est alors de n’utiliser que des informations issues de la géométrie des détections fragmentaires : localisation spatiale dans l’image et taille des détections. Une menace est alors supposée d’autant plus importante que les détections sont de tailles importantes et temporellement persistantes.Le cadre formel choisi est la théorie des fonctions de croyance qui permet de modéliser des données à la fois imprécises et incertaines. Les contributions de cette thèse concernent la représentation des objets en termes de localisation imprécise et incertaine et le filtrage des objets.La représentation pertinente des informations est un point clé pour les problèmes d’estimation ou la prise de décision. Une bonne représentation se reconnaît au fait qu’en découlent des critères simples et performants pour résoudre des sous-problèmes. La représentation proposée dans cette thèse a été valorisée par le fait qu’un critère d’association entre nouvelles détections (fragments) et objets en construction, a pu être défini d’une façon simple et rigoureuse. Rappelons que cette association est une étape clé pour de nombreux problèmes impliquant des données non étiquettées, ce qui étend notre contribution au-delà de l’application considérée.Le filtrage des données est utilisé dans de nombreuses méthodes ou algorithmes pour robustifier les résultats en s’appuyant sur la redondance attendue des données s’opposant à l’inconsistance du bruit. Nous avons alors formulé ce problème en termes d’estimation dynamique d’un cadre de discernement contenant les ‘vraies hypothèses’. Ce cadre est estimé dynamiquement avec la prise en compte de nouvelles données (ou observations) permettant de détecter deux principaux types d’erreurs : la duplication de certaines hypothèses (objets dans notre application), la présence de fausses alarmes (dues au bruit ou aux fausses détections dans notre cas).Pour finir nous montrons la possibilité de coupler nos briques de construction des objets et de filtrage de ces derniers avec une brique de suivi utilisant des informations plus haut niveau, telle que les algorithmes de tracking classiques de traitement d’image.Mots clés: théorie des fonctions des croyances, association de données, filtrage

Distances in evidence theory: Comprehensive survey and generalizations

AbstractThe purpose of the present work is to survey the dissimilarity measures defined so far in the mathematical framework of evidence theory, and to propose a classification of these measures based on their formal properties. This research is motivated by the fact that while dissimilarity measures have been widely studied and surveyed in the fields of probability theory and fuzzy set theory, no comprehensive survey is yet available for evidence theory. The main results presented herein include a synthesis of the properties of the measures defined so far in the scientific literature; the generalizations proposed naturally lead to additions to the body of the previously known measures, leading to the definition of numerous new measures. Building on this analysis, we have highlighted the fact that Dempster’s conflict cannot be considered as a genuine dissimilarity measure between two belief functions and have proposed an alternative based on a cosine function. Other original results include the justification of the use of two-dimensional indexes as (cosine; distance) couples and a general formulation for this class of new indexes. We base our exposition on a geometrical interpretation of evidence theory and show that most of the dissimilarity measures so far published are based on inner products, in some cases degenerated. Experimental results based on Monte Carlo simulations illustrate interesting relationships between existing measures

Adding Executable Context to Executable Architectures: Enabling an Executable Context Simulation Framework (ECSF)

A system that does not stand alone is represented by a complex entity of component combinations that interact with each other to execute a function. In today\u27s interconnected world, systems integrate with other systems - called a system-of-systems infrastructure: a network of interrelated systems that can often exhibit both predictable and unpredictable behavior. The current state-of-the-art evaluation process of these system-of-systems and their community of practitioners in the academic community are limited to static methods focused on defining who is doing what and where. However, to answer the questions of why and how a system operates within complex systems-of-systems interrelationships, a system\u27s architecture and context must be observed over time, its executable architecture, to discern effective predictable and unpredictable behavior. The objective of this research is to determine a method for evaluating a system\u27s executable architecture and assess the contribution and efficiency of the specified system before it is built. This research led to the development of concrete steps that synthesize the observance of the executable architecture, assessment recommendations provided by the North Atlantic Treaty Organization (NATO) Code of Best Practice for Command and Control (C2) Assessment, and the metrics for operational efficiency provided by the Military Missions and Means Framework. Based on the research herein, this synthesis is designed to evaluate and assess system-of-systems architectures in their operational context to provide quantitative results