Max-min interval systems of linear equations with bounded solution

Myšková, Helena. "Max-min interval systems of linear equations with bounded solution." Kybernetika 48.2 (2012): 299-308. <http://eudml.org/doc/247045>.

@article{Myšková2012,
abstract = {Max-min 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=\min \lbrace a,b\rbrace $. The notation $\mathbf \{A\}\otimes \mathbf \{x\}=\mathbf \{b\}$ represents an interval system of linear equations, where $\mathbf \{A\}=[\underline\{A\},\overline\{A\}]$, $\mathbf \{b\}=[\underline\{b\},\overline\{b\}]$ are given interval matrix and interval vector, respectively, and a solution is from a given interval vector $\mathbf \{x\}=[\underline\{x\},\overline\{x\}]$. We define six types of solvability of max-min interval systems with bounded solution and give necessary and sufficient conditions for them.},
author = {Myšková, Helena},
journal = {Kybernetika},
keywords = {max-min algebra; interval system; T6-vector; weak T6 solvability; strong T6 solvability; T7-vector; weak T7 solvability; strong T7 solvability; max-min algebra; interval system; weak solvability; strong solvability; linear equations; bounded solutions; T6-vector; weak T6 solvability; strong T6 solvability; T7-vector; weak T7 solvability; strong T7 solvability},
language = {eng},
number = {2},
pages = {299-308},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Max-min interval systems of linear equations with bounded solution},
url = {http://eudml.org/doc/247045},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Myšková, Helena
TI - Max-min interval systems of linear equations with bounded solution
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 2
SP - 299
EP - 308
AB - Max-min 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=\min \lbrace a,b\rbrace $. The notation $\mathbf {A}\otimes \mathbf {x}=\mathbf {b}$ represents an interval system of linear equations, where $\mathbf {A}=[\underline{A},\overline{A}]$, $\mathbf {b}=[\underline{b},\overline{b}]$ are given interval matrix and interval vector, respectively, and a solution is from a given interval vector $\mathbf {x}=[\underline{x},\overline{x}]$. We define six types of solvability of max-min interval systems with bounded solution and give necessary and sufficient conditions for them.
LA - eng
KW - max-min algebra; interval system; T6-vector; weak T6 solvability; strong T6 solvability; T7-vector; weak T7 solvability; strong T7 solvability; max-min algebra; interval system; weak solvability; strong solvability; linear equations; bounded solutions; T6-vector; weak T6 solvability; strong T6 solvability; T7-vector; weak T7 solvability; strong T7 solvability
UR - http://eudml.org/doc/247045
ER -