Analytical descriptions of quantifier solutions to interval linear systems of relations

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Analytical descriptions of quantifier solutions to interval linear systems of relations. / Sharaya, Irene A.; Shary, Sergey P.

In: Mathematics Open, Vol. 1, 2250004, 2022.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{dcf241398eeb4e5986e9234c00c943c1,

title = "Analytical descriptions of quantifier solutions to interval linear systems of relations",

abstract = "We study systems of relations of the form Ax σ b, where σ is a vector of binary relations with the components “=”, “≥”, and “≤”, while the parameters (elements of the matrix A and right-hand side vector b) are uncertain and can take values from prescribed intervals. What is considered to be the set of its solutions depends on which logical quantifier is associated with each interval-valued parameter and what is the order of the quantifier prefixes for specific parameters. For solution sets that correspond to the quantifier prefix of a general form, we present equivalent quantifier-free analytical descriptions in the classical interval arithmetic, in Kaucher complete interval arithmetic and in the usual real arithmetic.",

keywords = "Interval linear equation, Kaucher interval arithmetic, analytical description, classical interval arithmetic, interval linear inequality, interval linear system of relations, quantifier elimination, quantifier solution, solution set",

author = "Sharaya, {Irene A.} and Shary, {Sergey P.}",

note = "Sharaya, I. A. Analytical descriptions of quantifier solutions to interval linear systems of relations / I. A. Sharaya, S. P. Shary // Mathematics Open. – 2022. – Vol. 01. – DOI 10.1142/s2811007222500043.",

year = "2022",

doi = "10.1142/S2811007222500043",

language = "English",

volume = "1",

journal = "Mathematics Open",

issn = "2811-0072",

publisher = "World Scientific",

}

RIS

TY - JOUR

T1 - Analytical descriptions of quantifier solutions to interval linear systems of relations

AU - Sharaya, Irene A.

AU - Shary, Sergey P.

N1 - Sharaya, I. A. Analytical descriptions of quantifier solutions to interval linear systems of relations / I. A. Sharaya, S. P. Shary // Mathematics Open. – 2022. – Vol. 01. – DOI 10.1142/s2811007222500043.

PY - 2022

Y1 - 2022

N2 - We study systems of relations of the form Ax σ b, where σ is a vector of binary relations with the components “=”, “≥”, and “≤”, while the parameters (elements of the matrix A and right-hand side vector b) are uncertain and can take values from prescribed intervals. What is considered to be the set of its solutions depends on which logical quantifier is associated with each interval-valued parameter and what is the order of the quantifier prefixes for specific parameters. For solution sets that correspond to the quantifier prefix of a general form, we present equivalent quantifier-free analytical descriptions in the classical interval arithmetic, in Kaucher complete interval arithmetic and in the usual real arithmetic.

AB - We study systems of relations of the form Ax σ b, where σ is a vector of binary relations with the components “=”, “≥”, and “≤”, while the parameters (elements of the matrix A and right-hand side vector b) are uncertain and can take values from prescribed intervals. What is considered to be the set of its solutions depends on which logical quantifier is associated with each interval-valued parameter and what is the order of the quantifier prefixes for specific parameters. For solution sets that correspond to the quantifier prefix of a general form, we present equivalent quantifier-free analytical descriptions in the classical interval arithmetic, in Kaucher complete interval arithmetic and in the usual real arithmetic.

KW - Interval linear equation

KW - Kaucher interval arithmetic

KW - analytical description

KW - classical interval arithmetic

KW - interval linear inequality

KW - interval linear system of relations

KW - quantifier elimination

KW - quantifier solution

KW - solution set

UR - https://www.mendeley.com/catalogue/47e5bab3-ee79-3aa6-9768-b957c9299545/

UR - https://elibrary.ru/item.asp?id=59507243

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105005607514&origin=inward

U2 - 10.1142/S2811007222500043

DO - 10.1142/S2811007222500043

M3 - Article

VL - 1

JO - Mathematics Open

JF - Mathematics Open

SN - 2811-0072

M1 - 2250004

ER -

ID: 68452929