Implementing belief function computations

Haenni, Rolf; Lehmann, Norbert

doi:10.1002/int.10073

Cited by 24 publications

(10 citation statements)

References 18 publications

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“…By using plausibilities p Ω , the complexity is O(2 |Ω| T) [28]. As a recommendation, when |Ω| is large, it is preferable to avoid matrix calculus and use the binary format as means to encode focal elements [71], -Finally, it is assumed that sensors required for measuring the effectiveness are available. First, it might not be the case and one needs to assess cost/benefits of adding the required sensors.…”

Section: Discussionmentioning

confidence: 99%

Effectiveness assessment of Cyber-Physical Systems

Rocher

Tigli

Lavirotte

et al. 2020

International Journal of Approximate Reasoning

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By achieving their purposes through interactions with the physical world, Cyber-Physical Systems (CPS) pose new challenges in terms of dependability. Indeed, the evolution of the physical systems they control with transducers can be affected by surrounding physical processes over which they have no control and which may potentially hamper the achievement of their purposes. While it is illusory to hope for a comprehensive model of the physical environment at design time to anticipate and remove faults that may occur once these systems are deployed, it becomes necessary to evaluate their degree of effectiveness in vivo. In this paper, the degree of effectiveness is formally defined and generalized in the context of the measure theory. The measure is developed in the context of the Transferable Belief Model (TBM), an elaboration on the Dempster-Shafer Theory (DST) of evidence so as to handle epistemic and aleatory uncertainties respectively pertaining the users' expectations and the natural variability of the physical environment. The TBM is used in conjunction with the Input/Output Hidden Markov Modeling framework we denote by Ev-IOHMM to specify the expected evolution of the physical system controlled by the CPS and the tolerances towards uncertainties. The measure of effectiveness is then obtained from the forward algorithm, leveraging the conflict entailed by the successive combinations of the beliefs obtained from observations of the physical system and the beliefs corresponding to its expected evolution. The proposed approach is applied to autonomous vehicles and shows how the degree of effectiveness can be used for bench-marking their controller relative to the highway code speed limitations and passengers' well-being constraints, both modeled through an Ev-IOHMM.program issues the right commands to the computational resources. In this sense, a computer program is a perfect deterministic model of a computing system and the question does not even arise that, x being a variable, the execution of the following code snippet will lead its value to be set to 6 into the memory.

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Section: Discussionmentioning

confidence: 99%

Effectiveness assessment of Cyber-Physical Systems

Rocher

Tigli

Lavirotte

et al. 2020

International Journal of Approximate Reasoning

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“…Computationally, D-S networks are more expensive to evaluate than Bayesian networks [16,43]. The worst-case complexity of a Bayesian network is O(n), whereas the worst-case complexity of a D-S network is O(2 n ), with n the dimension of the state space of the largest clique in the join tree 5 [16].…”

Section: Computational Efficiencymentioning

confidence: 99%

Bayesian and Dempster–Shafer reasoning for knowledge-based fault diagnosis–A comparative study

Verbert

Babuka

Schutter

2017

Engineering Applications of Artificial Intelligence

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Even though various frameworks exist for reasoning under uncertainty, a realistic fault diagnosis task does not fit into any of them in a straightforward way. For each framework, only part of the available data and knowledge is in the desired format. Moreover, additional criteria, like clarity of inference and computational efficiency, require trade-offs to be made. Finally, fault diagnosis is usually just a subpart of a larger process, e.g. condition-based maintenance. Consequently, the final goal of fault diagnosis is not (just) decision making, and the outcome of the diagnosis process should be a suitable input for the subsequent reasoning process. In this chapter, we analyze how a knowledge-based diagnosis task is influenced by uncertainty, investigate which additional objectives are of relevance, and compare how these characteristics and objectives are handled in two well-known frameworks, namely the Bayesian and the Dempster-Shafer reasoning framework. In contrast to previous works, which take the reasoning method as the starting point, we start from the application, knowledge-based fault diagnosis, and examine the effectiveness of different reasoning methods for this specific application. It is concluded that the suitability of each reasoning method highly depends on the problem under consideration and on the requirements of the user. The best framework can only be assigned given that the problem (including uncertainty characteristics) and the user requirements are completely known.

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“…An alternative way that permits directly computing the bpa of an element A = ( A 1 , A 2 , …, A k ) of P ( Z ) is based on the application of the Dempster rule to the cylindrical extensions of the power sets elements. ( 26 ) The cylindrical extension A i ↑ of an element A i of Z i over Z is defined by considering for the variables x 1 , x 2 , …, x i −1 , x i +1 , …, x k their entire UODs: …”

Section: The Multiple‐assumptions Multiple‐experts Model Uncertainmentioning

confidence: 99%

A Comparison Between Probabilistic and Dempster-Shafer Theory Approaches to Model Uncertainty Analysis in the Performance Assessment of Radioactive Waste Repositories

Baraldi

Zio

2010

Risk Analysis

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Model uncertainty is a primary source of uncertainty in the assessment of the performance of repositories for the disposal of nuclear wastes, due to the complexity of the system and the large spatial and temporal scales involved. This work considers multiple assumptions on the system behavior and corresponding alternative plausible modeling hypotheses. To characterize the uncertainty in the correctness of the different hypotheses, the opinions of different experts are treated probabilistically or, in alternative, by the belief and plausibility functions of the Dempster-Shafer theory. A comparison is made with reference to a flow model for the evaluation of the hydraulic head distributions present at a radioactive waste repository site. Three experts are assumed available for the evaluation of the uncertainties associated with the hydrogeological properties of the repository and the groundwater flow mechanisms.

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Implementing belief function computations

Abstract: This article discusses several implementation aspects for Dempster-Shafer belief functions. The main objective is to propose an appropriate representation of mass functions and efficient data structures and algorithms for the two basic operations of combination and marginalization.

Cited by 24 publications

References 18 publications

Effectiveness assessment of Cyber-Physical Systems

Effectiveness assessment of Cyber-Physical Systems

Bayesian and Dempster–Shafer reasoning for knowledge-based fault diagnosis–A comparative study

A Comparison Between Probabilistic and Dempster-Shafer Theory Approaches to Model Uncertainty Analysis in the Performance Assessment of Radioactive Waste Repositories

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