Geodesic
Max-min interval systems of linear equations with bounded solution
Kybernetika, Tome 48 (2012) no. 2, pp. 299-308 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Max-min algebra is an algebraic structure in which classical addition and multiplication are replaced by $\oplus$ and $\otimes$, where $a\oplus b=\max\{a,b\},\ a\otimes b=\min\{a,b\}$. 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.
Max-min algebra is an algebraic structure in which classical addition and multiplication are replaced by $\oplus$ and $\otimes$, where $a\oplus b=\max\{a,b\},\ a\otimes b=\min\{a,b\}$. 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.
Classification : 15A06, 65G30
Keywords: max-min algebra; interval system; T6-vector; weak T6 solvability; strong T6 solvability; T7-vector; weak T7 solvability; strong T7 solvability 
@article{KYB_2012_48_2_a9,
     author = {My\v{s}kov\'a, Helena},
     title = {Max-min interval systems of linear equations with bounded solution},
     journal = {Kybernetika},
     pages = {299--308},
     year = {2012},
     volume = {48},
     number = {2},
     mrnumber = {2954328},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012_48_2_a9/}
}
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Myšková, Helena. Max-min interval systems of linear equations with bounded solution. Kybernetika, Tome 48 (2012) no. 2, pp. 299-308. http://geodesic.mathdoc.fr/item/KYB_2012_48_2_a9/