Clouds, p-boxes, Fuzzy Sets, and Other Uncertainty Representations in Higher Dimensions

@article{Fuchs2009CloudsPF,
  title={Clouds, p-boxes, Fuzzy Sets, and Other Uncertainty Representations in Higher Dimensions},
  author={Martin Fuchs},
  journal={Acta Cybern.},
  year={2009},
  volume={19},
  pages={61-92}
}
  • M. Fuchs
  • Published 2009
  • Computer Science
  • Acta Cybern.
Uncertainty modeling in real-life applications comprises some serious problems such as the curse of dimensionality and a lack of sufficient amount of statistical data. In this paper we give a survey of methods for uncertainty handling and elaborate the latest progress towards real-life applications with respect to the problems that come with it. We compare different methods and highlight their relationships. We introduce intuitively the concept of potential clouds, our latest approach which… 

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References

SHOWING 1-10 OF 124 REFERENCES
Clouds, Fuzzy Sets, and Probability Intervals
TLDR
The basic theoretical and numerical properties of clouds are discussed, and they are related to histograms, cumulative distribution functions, and likelihood ratios, and to consistent possibility and necessity measures of Jamison and Lodwick.
Potential Based Clouds in Robust Design Optimization
TLDR
This paper introduces in detail the clouds formalism as a means to process available uncertainty information reliably, even if limited in amount and possibly lacking a formal description, which enables a worst-case analysis with confidence regions of relevant scenarios which can be involved in an optimization problem formulation for robust design.
Relating practical representations of imprecise probabilities
TLDR
This paper mainly study the relationships between the two latter representations and the three other ones of probability families, including Ferson's p-boxes and Neumaier's clouds.
Combining Interval and Probabilistic Uncertainty: Foundations, Algorithms, Challenges { An Overview
TLDR
An overview of related algorithms, results, and remaining open problems relating to interval uncertainty and probabilistic uncertainty in the case when there is a combination of interval and probablistic uncertainty.
Computing expectations with p-boxes: two views of the same problem
TLDR
This paper focuses on p-boxes, a simple and popular model, and on lower expectations computed over non-monotone functions, and proposes tractable methods to compute approximations or exact values of these lower expectations.
A new Cauchy-based black-box technique for uncertainty in risk analysis
Monte-Carlo-Type Techniques for Processing Interval Uncertainty, and Their Potential Engineering Applications
TLDR
This work proposes to use special Monte-Carlo-type simulations to speed up the processing of sensitivity analysis in engineering applications, where the number n of uncertain parameters is huge, so sensitivity analysis leads to a lot of computation time.
Monte-Carlo-Type Techniques for Processing Interval Uncertainty , and Their Engineering Applications
In engineering applications, we need to make decisions under uncertainty. Traditionally, in engineering, statistical methods are used, methods assuming that we know the probability distribution of
Towards a unified theory of imprecise probability
  • P. Walley
  • Computer Science
    Int. J. Approx. Reason.
  • 2000
...
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