An iterative algorithm for testing solvability of max-min interval systems
Kybernetika (2012)
- Volume: 48, Issue: 5, page 879-889
- ISSN: 0023-5954
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topMyšková, Helena. "An iterative algorithm for testing solvability of max-min interval systems." Kybernetika 48.5 (2012): 879-889. <http://eudml.org/doc/251372>.
@article{Myšková2012,
abstract = {This paper is dealing with solvability of interval systems of linear equations in max-min algebra. Max-min algebra is the 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=\min \lbrace a, b\rbrace $. The notation $\{\mathbb \{A\}\}\otimes x=\{\mathbb \{b\}\}$ represents an interval system of linear equations, where $\{\mathbb \{A\}\}=[\underline\{A\},\overline\{A\}]$ 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 and T5 solvability and give necessary and sufficient conditions for them.},
author = {Myšková, Helena},
journal = {Kybernetika},
keywords = {max-min algebra; interval system; T4-vector; T4 solvability; T5-vector; T5 solvability; max-min algebra; interval system; T4-vector; T4 solvability; T5-vector; T5 solvability},
language = {eng},
number = {5},
pages = {879-889},
publisher = {Institute of Information Theory and Automation AS CR},
title = {An iterative algorithm for testing solvability of max-min interval systems},
url = {http://eudml.org/doc/251372},
volume = {48},
year = {2012},
}
TY - JOUR
AU - Myšková, Helena
TI - An iterative algorithm for testing solvability of max-min interval systems
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 5
SP - 879
EP - 889
AB - This paper is dealing with solvability of interval systems of linear equations in max-min algebra. Max-min algebra is the 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=\min \lbrace a, b\rbrace $. The notation ${\mathbb {A}}\otimes x={\mathbb {b}}$ represents an interval system of linear equations, where ${\mathbb {A}}=[\underline{A},\overline{A}]$ 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 and T5 solvability and give necessary and sufficient conditions for them.
LA - eng
KW - max-min algebra; interval system; T4-vector; T4 solvability; T5-vector; T5 solvability; max-min algebra; interval system; T4-vector; T4 solvability; T5-vector; T5 solvability
UR - http://eudml.org/doc/251372
ER -
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