# On an algorithm for testing T4 solvability of max-plus interval systems

Kybernetika (2012)

• Volume: 48, Issue: 5, page 924-938
• ISSN: 0023-5954

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## Abstract

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In this paper, we shall deal with the solvability of interval systems of linear equations in max-plus algebra. Max-plus algebra is an algebraic structure in which classical addition and multiplication are replaced by $\oplus$ and $\otimes$, where $a\oplus b=max\left\{a,b\right\}$, $a\otimes b=a+b$. The notation $𝔸\otimes x=𝕓$ represents an interval system of linear equations, where $𝔸=\left[\overline{b},\overline{A}\right]$ and $𝕓=\left[\underline{b},\overline{b}\right]$ are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 solvability and give an algorithm for checking the T4 solvability.

## How to cite

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Myšková, Helena. "On an algorithm for testing T4 solvability of max-plus interval systems." Kybernetika 48.5 (2012): 924-938. <http://eudml.org/doc/251371>.

@article{Myšková2012,
abstract = {In this paper, we shall deal with the solvability of interval systems of linear equations in max-plus algebra. Max-plus algebra is an algebraic structure in which classical addition and multiplication are replaced by $\oplus$ and $\otimes$, where $a\oplus b=\max \lbrace a,b\rbrace$, $a\otimes b=a+b$. The notation $\{\mathbb \{A\}\}\otimes x=\{\mathbb \{b\}\}$ represents an interval system of linear equations, where $\{\mathbb \{A\}\}=[\overline\{b\},\overline\{A\}]$ and $\{\mathbb \{b\}\}=[\underline\{b\},\overline\{b\}]$ are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 solvability and give an algorithm for checking the T4 solvability.},
author = {Myšková, Helena},
journal = {Kybernetika},
keywords = {max-plus algebra; interval system; T4 vector; T4 solvability; max-plus algebra; interval system; T4 vector; T4 solvability; iterative method; algorithm},
language = {eng},
number = {5},
pages = {924-938},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On an algorithm for testing T4 solvability of max-plus interval systems},
url = {http://eudml.org/doc/251371},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Myšková, Helena
TI - On an algorithm for testing T4 solvability of max-plus interval systems
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 5
SP - 924
EP - 938
AB - In this paper, we shall deal with the solvability of interval systems of linear equations in max-plus algebra. Max-plus algebra is an algebraic structure in which classical addition and multiplication are replaced by $\oplus$ and $\otimes$, where $a\oplus b=\max \lbrace a,b\rbrace$, $a\otimes b=a+b$. The notation ${\mathbb {A}}\otimes x={\mathbb {b}}$ represents an interval system of linear equations, where ${\mathbb {A}}=[\overline{b},\overline{A}]$ and ${\mathbb {b}}=[\underline{b},\overline{b}]$ are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 solvability and give an algorithm for checking the T4 solvability.
LA - eng
KW - max-plus algebra; interval system; T4 vector; T4 solvability; max-plus algebra; interval system; T4 vector; T4 solvability; iterative method; algorithm
UR - http://eudml.org/doc/251371
ER -

## References

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