ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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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

Imprecise probabilistic graphical models: Equivalent representations, inference algorithms and applications

Credal networks are probabilistic graphical models that extend Bayesian nets to deal with imprecision in probability, and can actually be regarded as sets of Bayesian nets. Credal nets appear to be powerful means to represent and deal with many important and challenging problems in uncertain reasoning. The counterpart of having more freedom in the modeling phase is an increased inferential complexity of inferences, e.g., the so-called belief updating becomes a hard task even on relatively simple topologies. In this thesis, I start my investigation on credal networks by considering equivalent representations of those models. More specifically, I first deliver a new graphical language, which is called decision-theoretic being inspired by the formalism of decision graphs, for a unified representation of credal networks of any kind. I also present another representation, which is called binarization, being in fact a reformulation of a credal network solely based on binary variables. Remarkably, I prove that if a credal net is first reformulated by its decision-theoretic representation and then by the corresponding binarization, the resulting representation is completely equivalent. An equivalence relation between Bayesian and credal nets, when the reason for the missingness of some of the variables in the Bayesian nets is unknown, is also provided. The developed equivalent representations are applied to inference problems. First, I show that, by a decision-theoretic formulation, the algorithms that have been already designed for credal networks, which are mostly referred to a specific class of models, called separately specified nets, can be generalized to credal networks of any kind. Similar formalisms are also employed to solve inference and classification problems with missing observations. I also present a state-ofthe-art updating algorithm which is based on the equivalent binary representation. This algorithm, called GL2U, offers an efficient procedure for approximate updating of general credal nets. The quality of the overall approximation is investigated by promising numerical experiments. As a further theoretical investigation, I consider a classification problem for Bayesian networks for which a hardness proof together with a fast algorithm for a subclass of models is provided.Finally, two real-world applications of credal networks are presented. First, I consider a military identification problem, consisting in the detection of the goal of an intruder entering a no-fly area. The problem, together with the necessary fusion of the information gathered by the sensors is mapped by our techniques into a credal network updating task. The solution is then obtained by the GL2U algorithm. The second application is an environmental model for hazard assessment of debris flows by credal networks. A credal network evaluates the level of risk, corresponding to the observed values of the triggering factors, for this specific natural hazard. For some factors, whose observations are more difficult, the corresponding soft evidential information is embedded by our formalism into the structure of the network. This model is employed for extensive numerical analysis on the Swiss territory