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Paper details
Number 3 - September 2017
Volume 27 - 2017
Is an interval the right result of arithmetic operations on intervals?
Andrzej Piegat, Marek Landowski
Abstract
For many scientists interval arithmetic (IA, I arithmetic) seems to be easy and simple. However, this is not true. Interval
arithmetic is complicated. This is confirmed by the fact that, for years, new, alternative versions of this arithmetic have been
created and published. These new versions tried to remove shortcomings and weaknesses of previously proposed options
of the arithmetic, which decreased the prestige not only of interval arithmetic itself, but also of fuzzy arithmetic, which,
to a great extent, is based on it. In our opinion, the main reason for the observed shortcomings of the present IA is the
assumption that the direct result of arithmetic operations on intervals is also an interval. However, the interval is not a direct
result but only a simplified representative (indicator) of the result. This hypothesis seems surprising, but investigations
prove that it is true. The paper shows what conditions should be satisfied by the result of interval arithmetic operations
to call it a “result”, how great its dimensionality is, how to perform arithmetic operations and solve equations. Examples
illustrate the proposed method of interval computations.
Keywords
interval arithmetic, one-dimensional interval arithmetic, multi-dimensional interval arithmetic, RDM interval arithmetic