Joint propagation of probability and possibility in risk analysis: Towards a formal framework

Baudrit, Cédric; Couso, Inés; Dubois, Didier

doi:10.1016/j.ijar.2006.07.001

Cited by 101 publications

(91 citation statements)

References 41 publications

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“…evaluating the impact of the uncertainty pervading the input on the outcome of the risk assessment model. To do so, the main function is PROPAG, which implements the Monte-Carlo-based algorithm of (Baudrit et al 2007) for jointly handling possibility and probability distributions and the algorithm of (Baudrit, Dubois, and Perrot 2008) for jointly handling possibility, probability distributions and p-boxes. Different options for summarizing and visualizing the results of this step are available, which are fully described in Section 5.…”

Section: Package Functionalitiesmentioning

confidence: 99%

“…When dealing with uncertainties, two facets should be considered as outlined by several authors. See for instance for seismic risk: Rohmer and Baudrit (2011), for volcano risks: Marzocchi, Sandri, Gasparini, Newhall, and Boschi (2004), for environmental risk: Baudrit, Couso, and Dubois (2007). The first facet corresponds to aleatory uncertainty (also named randomness or intrinsic variability).…”

Section: Introductionmentioning

confidence: 99%

“…(Ferson 1996;Helton, Johnson, and Oberkampf 2004;Baudrit 2005;Baudrit and Dubois 2006;Baudrit et al 2007;Dubois and Guyonnet 2011;Beer, Ferson, and Kreinovich 2013). In such highly uncertain situations, the challenge is to formulate appropriate mathematical tools and models in a quantitative manner, on the one hand, accounting for all data and pieces of information, but, on the other hand, without introducing unwarranted assumptions (Beer et al 2013).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

HYRISK: An R package for hybrid uncertainty analysis using probability, imprecise probability and possibility distributions

Rohmer¹,

manceau²,

Guyonnet³

et al. 2018

Preprint

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Uncertainty analysis is an unavoidable risk assessment task (for instance for natural hazards, or for environmental issues). In situations where data are scarce, incomplete or imprecise, the systematic and only use of probabilities can be debatable. Over the last years, several alternative mathematical representation methods have been developed to handle in a more flexible manner the lack of knowledge related to input parameters of risk assessment models. This article presents an R package HYRISK dedicated to jointly handling different mathematical representation tools, namely probabilities, possibility distributions and probability functions with imprecise parameters, for the different stages of uncertainty treatment in risk assessments (i.e. uncertainty representation, propagation, sensitivity analysis and decision-making). We support the description using the case study of a dike stability analysis. The package is available at: https://cran.r-project.org/web/packages/HYRISK/index.html.

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Section: Package Functionalitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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HYRISK: An R package for hybrid uncertainty analysis using probability, imprecise probability and possibility distributions

Rohmer¹,

manceau²,

Guyonnet³

et al. 2018

Preprint

View full text Add to dashboard Cite

show abstract

“…Finding the potential of possibilistic representations in computing conservative bounds for such probabilistic calculations is certainly a major challenge [99]. Methods for joint propagation of possibilistic and probabilistic information have been devised [9], based on casting both in a random set setting [6]; the case of probabilistic models with fuzzy interval parameters has also been dealt with [8]. The active area of fuzzy random variables is also connected to this question [95].…”

Section: Some Applicationsmentioning

confidence: 99%

Possibility Theory and Its Applications: Where Do We Stand?

Dubois

Prade

2015

Springer Handbook of Computational Intelligence

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148

101

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This paper provides an overview of possibility theory, emphasizing its historical roots and its recent developments. Possibility theory lies at the crossroads between fuzzy sets, probability and non-monotonic reasoning. Possibility theory can be cast either in an ordinal or in a numerical setting. Qualitative possibility theory is closely related to belief revision theory, and common-sense reasoning with exception-tainted knowledge in Artificial Intelligence. Possibilistic logic provides a rich representation setting, which enables the handling of lower bounds of possibility theory measures, while remaining close to classical logic. Qualitative possibility theory has been axiomatically justified in a decision-theoretic framework in the style of Savage, thus providing a foundation for qualitative decision theory. Quantitative possibility theory is the simplest framework for statistical reasoning with imprecise probabilities. As such it has close connections with random set theory and confidence intervals, and can provide a tool for uncertainty propagation with limited statistical or subjective information.

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“…Kruse and Meyer [47] clearly define the variance of a fuzzy random variable as a fuzzy set of positive reals induced by applying the extension principle to the variance formula. Likewise, the probability of an event becomes restricted by a fuzzy interval in the real line [1,14]. The evidence theory counterpart of this view deals with belief functions having fuzzy focal elements [75].…”

Section: Various Notions Of Random Fuzzy Setsmentioning

confidence: 99%

Statistical reasoning with set-valued information: Ontic vs. epistemic views

Couso

Dubois

2014

International Journal of Approximate Reasoning

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161

111

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. In information processing tasks, sets may have a conjunctive or a disjunctive reading. In the conjunctive reading, a set represents an object of interest and its elements are subparts of the object, forming a composite description. In the disjunctive reading, a set contains mutually exclusive elements and refers to the representation of incomplete knowledge. It does not model an actual object or quantity, but partial information about an underlying object or a precise quantity. This distinction between what we call ontic vs. epistemic sets remains valid for fuzzy sets, whose membership functions, in the disjunctive reading are possibility distributions, over deterministic or random values. This paper examines the impact of this distinction in statistics. We show its importance because there is a risk of misusing basic notions and tools, such as conditioning, distance between sets, variance, regression, etc. when data are set-valued. We discuss several examples where the ontic and epistemic points of view yield different approaches to these concepts.

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Joint propagation of probability and possibility in risk analysis: Towards a formal framework

Cited by 101 publications

References 41 publications

HYRISK: An R package for hybrid uncertainty analysis using probability, imprecise probability and possibility distributions

HYRISK: An R package for hybrid uncertainty analysis using probability, imprecise probability and possibility distributions

Possibility Theory and Its Applications: Where Do We Stand?

Statistical reasoning with set-valued information: Ontic vs. epistemic views

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