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Register a new userCurrent Trends and Applications of Dempster-Shafer Theory (Review)
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Vladimir Ivanov
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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The article provides a review of the publications on the current trends and developments in Dempster-Shafer theory and its different applications in science, engineering, and technologies. The review took account of the following provisions with a focus on some specific aspects of the theory. Firstly, the article considers the research directions whose results are known not only in scientific and academic community but understood by a wide circle of potential designers and developers of advanced engineering solutions and technologies. Secondly, the article shows the theory applications in some important areas of human activity such as manufacturing systems, diagnostics of technological processes, materials and products, building and construction, product quality control, economic and social systems. The particular attention is paid to the current state of research in the domains under consideration and, thus, the papers published, as a rule, in recent years and presenting the achievements of modern research on Dempster-Shafer theory and its application are selected and analyzed.
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Dempster-Shafer Theory (DST) generalizes Bayesian probability theory, offering useful additional information, but suffers from a high computational burden. A lot of work has been done to reduce the complexity of computations used in information fusion with Dempsters rule. The main approaches exploit either the structure of Boolean lattices or the information contained in belief sources. Each has its merits depending on the situation. In this paper, we propose sequences of graphs for the computation of the zeta and Mobius transformations that optimally exploit both the structure of distributive semilattices and the information contained in belief sources. We call them the Efficient Mobius Transformations (EMT). We show that the complexity of the EMT is always inferior to the complexity of algorithms that consider the whole lattice, such as the Fast Mobius Transform (FMT) for all DST transformations. We then explain how to use them to fuse two belief sources. More generally, our EMTs apply to any function in any finite distributive lattice, focusing on a meet-closed or join-closed subset. This article extends our work published at the international conference on Scalable Uncertainty Management (SUM). It clarifies it, brings some minor corrections and provides implementation details such as data structures and algorithms applied to DST.
Dempster-Shafer Theory (DST) generalizes Bayesian probability theory, offering useful additional information, but suffers from a much higher computational burden. A lot of work has been done to reduce the time complexity of information fusion with Dempsters rule, which is a pointwise multiplication of two zeta transforms, and optimal general algorithms have been found to get the complete definition of these transforms. Yet, it is shown in this paper that the zeta transform and its inverse, the Mobius transform, can be exactly simplified, fitting the quantity of information contained in belief functions. Beyond that, this simplification actually works for any function on any partially ordered set. It relies on a new notion that we call focal point and that constitutes the smallest domain on which both the zeta and Mobius transforms can be defined. We demonstrate the interest of these general results for DST, not only for the reduction in complexity of most transformations between belief representations and their fusion, but also for theoretical purposes. Indeed, we provide a new generalization of the conjunctive decomposition of evidence and formulas uncovering how each decomposition weight is tied to the corresponding mass function.
Automated negotiation can be an efficient method for resolving conflict and redistributing resources in a coalition setting. Automated negotiation has already seen increased usage in fields such as e-commerce and power distribution in smart girds, and recent advancements in opponent modelling have proven to deliver better outcomes. However, significant barriers to more widespread adoption remain, such as lack of predictable outcome over time and user trust. Additionally, there have been many recent advancements in the field of reasoning about uncertainty, which could help alleviate both those problems. As there is no recent survey on these two fields, and specifically not on their possible intersection we aim to provide such a survey here.
The orthocomplemented modular lattice of subspaces L[H(d)], of a quantum system with d- dimensional Hilbert space H(d), is considered. A generalized additivity relation which holds for Kolmogorov probabilities, is violated by quantum probabilities in the full lattice L[H(d)] (it is only valid within the Boolean subalgebras of L[H(d)]). This suggests the use of more general (than Kolmogorov) probability theories, and here the Dempster-Shafer probability theory is adopted. An operator D(H1,H2), which quantifies deviations from Kolmogorov probability theory is introduced, and it is shown to be intimately related to the commutator of the projectors P(H1),P(H2), to the subspaces H1,H2. As an application, it is shown that the proof of CHSH inequalities for a system of two spin 1/2 particles, is valid for Kolmogorov probabilities, but it is not valid for Dempster- Shafer probabilities. The violation of these inequalities in experiments, supports the interpretation of quantum probabilities as Dempster-Shafer probabilities.
With populations ageing, the number of people with dementia worldwide is expected to triple to 152 million by 2050. Seventy percent of cases are due to Alzheimers disease (AD) pathology and there is a 10-20 year pre-clinical period before significant cognitive decline occurs. We urgently need, cost effective, objective methods to detect AD, and other dementias, at an early stage. Risk factor modification could prevent 40% of cases and drug trials would have greater chances of success if participants are recruited at an earlier stage. Currently, detection of dementia is largely by pen and paper cognitive tests but these are time consuming and insensitive to pre-clinical phases. Specialist brain scans and body fluid biomarkers can detect the earliest stages of dementia but are too invasive or expensive for widespread use. With the advancement of technology, Artificial Intelligence (AI) shows promising results in assisting with detection of early-stage dementia. Existing AI-aided methods and potential future research directions are reviewed and discussed.
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