A realistic quantification of all input information is a basic requirement in order to obtain useful results from engineering analyses. The concept of quantification and the associated uncertainty model have to be selected in agreement with the amount and quality of the available information. For inconsistent information, a distinction between probabilistic and non-probabilistic characteristics is beneficial. In this distinction, uncertainty refers to probabilistic characteristics and non-probabilistic characteristics are summarized as imprecision. When uncertainty and imprecision occur simultaneously, the uncertainty model fuzzy randomness appears useful. In this paper, the fuzzy probabilistic model is utilized in a Bayesian approach to take account of imprecision in data and in prior expert knowledge. The propagation of imprecision and uncertainty is investigated for selected cases. The Bayesian approach extended to inconsistent information is demonstrated by means of an example.
Bayesian Update With Fuzzy Information
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Beer, M, & Stein, M. "Bayesian Update With Fuzzy Information." Proceedings of the ASME 2011 International Mechanical Engineering Congress and Exposition. Volume 9: Transportation Systems; Safety Engineering, Risk Analysis and Reliability Methods; Applied Stochastic Optimization, Uncertainty and Probability. Denver, Colorado, USA. November 11–17, 2011. pp. 821-829. ASME. https://doi.org/10.1115/IMECE2011-62424
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