Rejoinder to comments on “reasoning with belief functions: An analysis of compatibility”

AbstractAn earlier position paper has examined the applicability of belief-functions methodology in three reasoning tasks: (1) representation of incomplete knowledge, (2) belief-updating, and (3) evidence pooling. My conclusions were that the use of belief functions encounters basic difficulties along all three tasks, and that extensive experimental and theoretical studies should be undertaken before belief functions could be applied safely. This article responds to the discussion, in this issue, of my conclusions and the degree to which they affect the applicability of belief functions in automated reasoning tasks

Information fusion schemes for real time risk assessment in adaptive control systems

Intelligent Flight Control System (IFCS) deploys a neural network for in-flight aircraft failure accommodation. Verification and validation (V&V) of adaptive systems is a challenging research problem. Our approach to V&V relies on real-time monitoring of neural network learning. Monitors detect learning anomalies and react to different failure conditions. We investigated data fusion techniques suitable for the analysis of neural network monitors. Monitor outputs are fused into a measure of confidence, indicating the belief in the correctness of failure accommodation mechanism provided by the neural network. We investigated two data fusion techniques, one based on Dempster-Shafer theory and the other based on fuzzy logic. Our techniques were applied to nine flight simulation datasets including those with failures. The monitor fusion algorithms provide unique, meaningful and novel technique for V&V of adaptive flight control systems. Being theoretically sound, the algorithms can be applied to a broad range of other data fusion applications

TPM: Cloud-Based Tele PTSD Monitor Using Multi-Dimensional Information

An automated system that can remotely and non-intrusively screen individuals at high risk for Post-Traumatic Stress Disorder (PTSD) and monitor their progress during treatment would be desired by many Veterans Affairs (VAs) as well as other PTSD treatment and research organizations. In this paper, we present an automated, cloud-based Tele-PTSD Monitor (TPM) system based on the fusion of multiple sources of information. The TPM system can be hosted in a cloud environment and accessed through landline or cell phones, or on the Internet through a web portal or mobile application (app)

Uncertain inference using interval probability theory

AbstractThe use of interval probability theory (IPT) for uncertain inference is demonstrated. The general inference rule adopted is the theorem of total probability. This enables information on the relevance of the elements of the power set of evidence to be combined with the measures of the support for and dependence between each item of evidence. The approach recognises the importance of the structure of inference problems and yet is an open world theory in which the domain need not be completely specified in order to obtain meaningful inferences. IPT is used to manipulate conflicting evidence and to merge evidence on the dependability of a process with the data handled by that process. Uncertain inference using IPT is compared with Bayesian inference

Death of Paradox: The Killer Logic Beneath the Standards of Proof

The prevailing but contested view of proof standards is that factfinders should determine facts by probabilistic reasoning. Given imperfect evidence, they should ask themselves what they think the chances are that the burdened party would be right if the truth were to become known; they then compare those chances to the applicable standard of proof. I contend that for understanding the standards of proof, the modern versions of logic — in particular, fuzzy logic and belief functions — work better than classical probability. This modern logic suggests that factfinders view evidence of an imprecisely perceived and described reality to form a fuzzy degree of belief in a fact’s existence; they then apply the standard of proof in accordance with the theory of belief functions, by comparing their belief in a fact’s existence to their belief in its negation. This understanding explains how the standard of proof actually works in the law world. It gives a superior mental image of the factfinders’ task, conforms more closely to what we know of people’s cognition, and captures better what the law says its standards are and how it manipulates them. One virtue of this conceptualization is that it is not a radically new view. Another virtue is that it nevertheless manages to resolve some stubborn problems of proof, including the infamous conjunction paradox

A logic-based analysis of Dempster-Shafer theory

AbstractDempster-Shafer (DS) theory is formulated in terms of propositional logic, using the implicit notion of provability underlying DS theory. Dempster-Shafer theory can be modeled in terms of propositional logic by the tuple (Σ, ϱ), where Σ is a set of propositional clauses and ϱ is an assignment of mass to each clause Σi ϵ Σ. It is shown that the disjunction of minimal support clauses for a clause Σi with respect to a set Σ of propositional clauses, ξ(Σi, Σ), when represented in terms of symbols for the ϱi 's, corresponds to a symbolic representation of the Dempster-Shafer belief function for δi. The combination of Belief functions using Dempster's rule of combination corresponds to a combination of the corresponding support clauses. The disjointness of the Boolean formulas representing DS Belief functions is shown to be necessary. Methods of computing disjoint formulas using network reliability techniques are discussed.In addition, the computational complexity of deriving DS Belief functions, including that of the logic-based methods which are the focus of this paper, is explored. Because of intractability even for moderately sized problem instances, efficient approximation methods are proposed for such computations. Finally, implementations of DS theory based on domain restrictions of DS theory, hypertree embeddings, and the ATMS, are examined

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