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Verified stochastic methods

Markov set-chains and dependency modeling of mean and standard deviation

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Abstract

Markov chains provide quite attractive features for simulating a system’s behavior under consideration of uncertainties. However, their use is somewhat limited because of their deterministic transition matrices. Vague probabilistic information and imprecision appear in the modeling of real-life systems, thus causing difficulties in the pure probabilistic model set-up. Moreover, their accuracy suffers due to implementations on computers with floating point arithmetics. Our goal is to address these problems by extending the Dempster-Shafer with Intervals toolbox for MATLAB with novel verified algorithms for modeling that work with Markov chains with imprecise transition matrices, known as Markov set-chains. Additionally, in order to provide a statistical estimation tool that can handle imprecision to set up Markov chain models, we develop a new verified algorithm for computing relations between the mean and the standard deviation of fuzzy sets.

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Acknowledgments

We would like to thank the anonymous reviewers for their constructive comments and suggestions that have highly improved the quality of earlier drafts.

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Authors and Affiliations

  1. Computer and Cognitive Science (INKO), University of Duisburg-Essen, Duisburg, Germany

    Gabor Rebner & Ekaterina Auer

  2. Institute for Risk and Uncertainty, University of Liverpool, Liverpool, UK

    Michael Beer

  3. Department of Civil and Environmental Engineering, National University of Singapore, Singapore, Singapore

    Matthias Stein

Authors
  1. Gabor Rebner
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  2. Michael Beer
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  3. Ekaterina Auer
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  4. Matthias Stein
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Corresponding author

Correspondence to Gabor Rebner.

Additional information

Communicated by V. Kreinovich.

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Rebner, G., Beer, M., Auer, E. et al. Verified stochastic methods. Soft Comput 17, 1415–1423 (2013). https://doi.org/10.1007/s00500-013-1009-7

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  • DOI: https://doi.org/10.1007/s00500-013-1009-7

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