Дослідження закону дистрибутивності в розширеному інтервальному просторі

Authors

  • Ольга Анатоліївна Жуковська NTUU KPI, Ukraine

DOI:

https://doi.org/10.20535/1810-0546.2014.4.28304

Keywords:

Intervals, Distributive law

Abstract

A study of the law of distributivity in the extended interval space is suggested. The research for interval in the center–radius form was conducted. The classification of the intervals is proposed. A set of intervals is represented as a union of three subsets which have defined by the relations of values the centers and the radii. We proved the lemma about the conditions under which the sum of the two intervals will own to same subset of the intervals you want to add. The conditions in which the sum of the two intervals belongs to the same subset as intervals, which are added. The necessary and sufficient conditions for the distributive law hold for the intervals belonging to one of the subsets are offered. A numerical example demonstrating, that the obtained conditions are constructive, is                presented. These results provide the opportunity to conduct research to improve the algebraic structure of the set of intervals.

Author Biography

Ольга Анатоліївна Жуковська, NTUU KPI

Candidate of sciences (physics and mathematics), PhD, associate professor, assistant professor at the NTUU KPI

References

Прикладной интервальный анализ / Л. Жолен, М. Ки­фер, О. Дидри, Э. Вальтер. – М.; Ижевск: Ин-т компьютерных исследований, 2005. – 468 с.

S.M. Markov, “Extended Interval Arithmetic Involving Infinite Intervals”, Math. Balkanika, New Ser., vol. 6, pp. 269–304, 1992.

E.D. Popova, Generalized Interval Distributive Relations, Institute of Mathematics&Computer Science, Bulgarian Academy of Sciences. Bulgaria, 1997, preprint no. 2, 18 p.

Жуковська О.А., Титаренко А.О. Дослідження закону дистрибутивності в класичній інтервальній арифметиці для загального випадку // Наукові вісті НТУУ “КПІ”. – 2013. – № 4. – С. 38–44.

Жуковська О.А. Дослідження інтервальних арифметичних операцій в класичному та розширеному просторах // Збірник праць Ін-ту математики НАНУ. – 2008. – 5, № 5. – С. 85–110.

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Published

2014-08-19

Issue

No. 4 (2014): Physics and Mathematics

Section

Art

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