Fuzzy randomness – a contribution to imprecise probability

Möller, Bernd

doi:10.1002/zamm.200410153

Cited by 16 publications

(10 citation statements)

References 7 publications

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“…In the MC-FIA approach, the propagation of the hybrid uncertainty is performed by combining the MC technique 34,35 with the extension principle of fuzzy set theory [36][37][38][39][40][41][42][43][44][45] within a "level-2" setting by means of the following main steps: 24,[46][47][48][49][50][51] (1) select one possibility value 1 ∈ (0, 1] and the corresponding cuts propagation method clearly assumes independence between the group of probabilistic (i.e., aleatory or random) variables and the group of the possibilistic (i.e., epistemicallyuncertain) parameters of the aleatory probability distributions.…”

Section: Hybrid Monte Carlo and Fuzzy Interval Analysis Approachmentioning

confidence: 99%

“…The main steps of the procedure are: 24,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51] (1) set 1 = 0 (outer loop processing epistemic uncertainty by fuzzy interval analysis); …”

Section: Appendix B Hybrid Monte Carlo and Fuzzy Interval Analysis Amentioning

confidence: 99%

“…[23][24][25][26] When both aleatory and epistemic uncertainties are represented by probability distributions, their propagation is carried out by a two-dimensional (or double) Monte Carlo (MC) simulation approach. 5,32,33 Instead, when a hybrid (probabilistic and possibilistic) uncertainty representation is considered, two approaches are here undertaken: (i) the hybrid MC and Fuzzy Interval Analysis (FIA) approach, b where the MC technique 34,35 is combined with the extension principle of fuzzy set theory, [36][37][38][39][40][41][42][43][44][45] within a "level-2" hierarchical setting; 24,[46][47][48][49][50][51] (ii) the Monte Carlo (MC)-based Dempster-Shafer (DS) approach employing Independent Random Sets (IRSs), c where the possibility distributions describing the epistemically-uncertain parameters are discretized into focal sets that are randomly and independently sampled by MC.…”

Section: Introductionmentioning

confidence: 99%

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Empirical Comparison of Methods for the Hierarchical Propagation of Hybrid Uncertainty in Risk Assessment, in Presence of Dependences

Pedroni

Zio

2012

Int. J. Unc. Fuzz. Knowl. Based Syst.

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Risk analysis models describing aleatory (i.e., random) events contain parameters (e.g., probabilities, failure rates, …) that are epistemically-uncertain, i.e., known with poor precision. Whereas aleatory uncertainty is always described by probability distributions, epistemic uncertainty may be represented in different ways (e.g., probabilistic or possibilistic), depending on the information and data available. The work presented in this paper addresses the issue of accounting for (in)dependence relationships between epistemically-uncertain parameters. When a probabilistic representation of epistemic uncertainty is considered, uncertainty propagation is carried out by a two-dimensional (or double) Monte Carlo (MC) simulation approach; instead, when possibility distributions are used, two approaches are undertaken: the hybrid MC and Fuzzy Interval Analysis (FIA) method and the MCbased Dempster-Shafer (DS) approach employing Independent Random Sets (IRSs). The objectives are: i) studying the effects of (in)dependence between the epistemically-uncertain parameters of the aleatory probability distributions (when a probabilistic/possibilistic representation of epistemic uncertainty is adopted) and ii) studying the effect of the probabilistic/possibilistic representation of epistemic uncertainty (when the state of dependence between the epistemic parameters is defined). The Dependency Bound Convolution (DBC) approach is then undertaken within a hierarchical setting of hybrid (probabilistic and possibilistic) uncertainty propagation, in order to account for all kinds of (possibly unknown) dependences between the random variables. The analyses are carried out with reference to two toy examples, built in such a way to allow performing a fair quantitative comparison between the methods, and evaluating their rationale and appropriateness in relation to risk analysis.

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Section: Hybrid Monte Carlo and Fuzzy Interval Analysis Approachmentioning

confidence: 99%

Section: Appendix B Hybrid Monte Carlo and Fuzzy Interval Analysis Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Empirical Comparison of Methods for the Hierarchical Propagation of Hybrid Uncertainty in Risk Assessment, in Presence of Dependences

Pedroni

Zio

2012

Int. J. Unc. Fuzz. Knowl. Based Syst.

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“…(2.73) may be described with the aid of fuzzy probability distribution functions. The fuzzy probability distribution function form I may be advantageously applied, amongst others, in structural analysis [36,38], in the Fuzzy Stochastic Finite Element Method (FSFEM) [35,62] and in the safety assessment of structures [39,63]. [36,66].…”

Section: Fuzzy Probability Distribution Functions Of Fuzzy Random Varmentioning

confidence: 99%

Uncertainty Forecasting in Engineering

Moeller¹,

Möller²,

Reuter³

2007

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“…The most commonly used methods include probability bound analysis [96] (also referred to as p-box approach, method of lower and upper previsions [97] or interval probabilities [98]), random set theory [99,100] (also referred to as evidence theory), and fuzzy randomness [101][102][103][104]. Mixed methods are not treated in the present work.…”

Section: Modeling Of Uncertaintiesmentioning

confidence: 99%

Dealing with uncertainty in model updating for damage assessment: A review

Simoen

Roeck

Lombaert

2015

Mechanical Systems and Signal Processing

397

217

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In structural engineering, model updating is often used for non-destructive damage assessment: by calibrating stiffness parameters of finite element models based on experimentally obtained (modal) data, structural damage can be identified, quantified and located. However, the model updating problem is an inverse problem prone to ill-posedness and ill-conditioning. This means the problem is extremely sensitive to small errors, which may potentially detract from the method's robustness and reliability. As many errors or uncertainties are present in model updating, both regarding the measurements as well as the employed numerical model, it is important to take these uncertainties suitably into account. This paper aims to provide an overview of the available approaches to this end, where two methods are treated in detail: a non-probabilistic fuzzy approach and a probabilistic Bayesian approach. These methods are both elaborated for the specific case of vibration-based finite element model updating for damage assessment purposes.

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Fuzzy randomness – a contribution to imprecise probability

Cited by 16 publications

References 7 publications

Empirical Comparison of Methods for the Hierarchical Propagation of Hybrid Uncertainty in Risk Assessment, in Presence of Dependences

Empirical Comparison of Methods for the Hierarchical Propagation of Hybrid Uncertainty in Risk Assessment, in Presence of Dependences

Uncertainty Forecasting in Engineering

Dealing with uncertainty in model updating for damage assessment: A review

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