Nested Intervals and Sets: Concepts, Relations to Fuzzy Sets, and Applications

  • Hung T. Nguyen
  • Vladik Kreinovich
Part of the Applied Optimization book series (APOP, volume 3)

Abstract

In data processing, we often encounter the following problem: Suppose that we have processed the measurement results \({\tilde x_1},...,{\tilde x_n}\), and, from this processing, have obtained an estimate \(\tilde y = f({\tilde x_1},...,{\tilde x_n})\) for a quantity y = f(xi,…,xn); we know the intervals xi of possible values of x i, and we want to find the interval y of possible values of y. Interval computations are one of the main techniques for solving this problem.

In some cases, for each i, in addition to the guaranteed interval xi of possible values, we have a smaller interval that an expert believes to contain x i. There may be several such nested intervals. In these cases, in addition to the guaranteed interval y, it is desirable to know the possible intervals of y that correspond to the opinions of different experts.

Techniques of such nested interval computations and real-life applications of these techniques are described in this paper.

Keywords

Transportation SerA Guaran Kalinin Blin 

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Hung T. Nguyen
    • 1
  • Vladik Kreinovich
    • 2
  1. 1.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA
  2. 2.Department of Computer ScienceUniversity of Texas at El PasoEl PasoUSA

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