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On Joint Modelling of Random Uncertainty and Fuzzy Imprecision

In: Coping with Uncertainty

Author

Listed:
  • Olgierd Hryniewicz

    (Systems Research Institute)

Abstract

The paper deals with the problem of the mathematical description of uncertainties of different type. It has been demonstrated by many authors that the theory of probability is not always suitable for the description of uncertainty related to vagueness. We briefly present some of the most promising theories which have been recently proposed for coping with this problem. Then, we concentrate our attention on the application of fuzzy random variables which seem to be very useful for the joint modelling of random uncertainty and fuzzy imprecision, and for the statistical analysis of imprecise data. The application of the statistical methodology for fuzzy data, called fuzzy statistics, is illustrated with two practical examples, typical for the problems of systems analysis. First example is devoted to the problem of the estimation of greenhouse gases inventories. In the second example, typical for the problems of making decisions using small amount of available data, we show how fuzzy approach can be used for the improvement of sequential statistical tests.

Suggested Citation

  • Olgierd Hryniewicz, 2010. "On Joint Modelling of Random Uncertainty and Fuzzy Imprecision," Lecture Notes in Economics and Mathematical Systems, in: Kurt Marti & Yuri Ermoliev & Marek Makowski (ed.), Coping with Uncertainty, chapter 0, pages 11-38, Springer.
    • Handle: RePEc:spr:lnechp:978-3-642-03735-1_2
    DOI: 10.1007/978-3-642-03735-1_2
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