Applications of Interval Computations pp 245-290 | Cite as

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

## 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 x_{i} 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 x_{i} 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## Preview

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