TY - JOUR

T1 - Non-Traditional Intervals and Their Use. Which Ones Really Make Sense?

AU - Shary, S. P.

N1 - © 2023, Pleiades Publishing, Ltd.

PY - 2023/6

Y1 - 2023/6

N2 - The paper discusses the question of why intervals, which are the main object of Interval Analysis, have exactly the form that we know well and habitually use, and not some other. In particular, we investigate why traditional intervals are closed, i.e., contain their endpoints, and also what is wrong with an empty interval. A second question considered in the work is how expedient it is to expand the set of traditional intervals by some other objects. We show that improper (“reversed”) intervals and the arithmetic of such intervals (the Kaucher complete interval arithmetic) are very useful from many different points of view.

AB - The paper discusses the question of why intervals, which are the main object of Interval Analysis, have exactly the form that we know well and habitually use, and not some other. In particular, we investigate why traditional intervals are closed, i.e., contain their endpoints, and also what is wrong with an empty interval. A second question considered in the work is how expedient it is to expand the set of traditional intervals by some other objects. We show that improper (“reversed”) intervals and the arithmetic of such intervals (the Kaucher complete interval arithmetic) are very useful from many different points of view.

KW - Kaucher interval arithmetic

KW - classical interval arithmetic

KW - interval

KW - interval analysis

KW - non-traditional intervals

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85165220855&origin=inward&txGid=dfc524952dddb887d6c6871c1a021c7a

UR - https://www.mendeley.com/catalogue/7bc32391-b214-3d3e-a547-86acfc29b292/

U2 - 10.1134/S1995423923020088

DO - 10.1134/S1995423923020088

M3 - Article

VL - 16

SP - 179

EP - 191

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 2

ER -