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Beyond Interval Uncertainty: Taking Constraints into Account

  • Hung T. Nguyen
  • Vladik Kreinovich
  • Berlin Wu
  • Gang Xiang
Part of the Studies in Computational Intelligence book series (SCI, volume 393)

Abstract

For set information, in addition to the interval bounds on each variables x1,..., x n , we may have additional information: e.g., we may know that the actual values should satisfy a constraint g(x1,..., x n ) ≤ g0. As we have mentioned earlier, usually, we know the approximate values of x i , so we can safely replace the function g(x1,..., x n ) by, e.g., the first two terms in its Taylor expansion. In this case, the constraint becomes quadratic, and – in a realistic case when this constraint describes a bounded set – the set of all the tuples x = (x1,..., x n ) that satisfy this constraint forms an ellipsoid. In this case, in addition to knowing that the actual tuple x belongs to the box, we also know that it belongs to the ellipsoid – i.e., that the set of possible values of this tuple is an intersection of the box and the ellipsoid. Such a situation is analyzed in this chapter.

Keywords

Linear Function Taylor Expansion Linear Time Interval Uncertainty Interval Bound 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hung T. Nguyen
    • Vladik Kreinovich
      • Berlin Wu
        • Gang Xiang

          There are no affiliations available

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