Geodesic
On an algorithm for testing T4 solvability of max-plus interval systems
Kybernetika, Tome 48 (2012) no. 5, pp. 924-938 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $a\oplus b=\max\{a,b\}$, $a\otimes b=a+b$. 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.
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 $a\oplus b=\max\{a,b\}$, $a\otimes b=a+b$. 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.
Classification : 15A06, 65G30
Keywords: max-plus algebra; interval system; T4 vector; T4 solvability 
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Myšková, Helena. On an algorithm for testing T4 solvability of max-plus interval systems. Kybernetika, Tome 48 (2012) no. 5, pp. 924-938. http://geodesic.mathdoc.fr/item/KYB_2012_48_5_a6/

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