Abstract
A probabilistic approach to the comparison of two intervals is developed. The method is based on the assumption that random variables are independently and uniformly distributed at given intervals. It allows all possible cases of interval location and intersection and of ordering of interval and real number to be taken into account. Additionally, this method allows the widths of the intervals to be taken into account in the ordering procedure. It should be noted that the probabilistic approach was used only to infer the set of formulae needed to estimate quantitatively the degree to which one interval is less or equal to another interval. The measure of such a degree may be treated formally as one of probability, but the term “possibility” can be also used, as it better reflects the sense of the relation between the intervals in many cases.
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Sevastjanov, P.V., Róg, P., Venberg, A.V. (2002). A Constructive Numerical Method for the Comparison of Intervals. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2001. Lecture Notes in Computer Science, vol 2328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48086-2_84
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DOI: https://doi.org/10.1007/3-540-48086-2_84
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