Is an interval the right result of arithmetic operations on intervals?

• Autorzy: Piegat A. , Landowski M.

Identyfikatory

DOI

10.1515/amcs-2017-0041

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

interval arithmetic; one dimensional interval arithmetic; multidimensional interval arithmetic; RDM interval arithmetic

PL

arytmetyka interwałowa; arytmetyka interwałowa jednowymiarowa; arytmetyka interwałowa wielowymiarowa

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2017
• Tom: Vol. 27, no. 3
• Strony: 575--590
• Opis fizyczny: Bibliogr. 33 poz., rys., wykr.

Twórcy

autor

Piegat A.

• Faculty of Computer Science, West Pomeranian University of Technology, Żołnierska 49, 71-210 Szczecin, Poland

autor

Landowski M.

• Department of Mathematical Methods, Maritime University of Szczecin, Wały Chrobrego 1–2, 70-500 Szczecin, Poland

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).