Geodesic
An iterative algorithm for testing solvability of max-min interval systems
Kybernetika, Tome 48 (2012) no. 5, pp. 879-889 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $a\oplus b=\max\{a,b\}, a\otimes b=\min\{a, b\}$. 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.
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 $a\oplus b=\max\{a,b\}, a\otimes b=\min\{a, b\}$. 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.
Classification : 15A06, 65G30
Keywords: max-min algebra; interval system; T4-vector; T4 solvability; T5-vector; T5 solvability 
@article{KYB_2012_48_5_a3,
     author = {My\v{s}kov\'a, Helena},
     title = {An iterative algorithm for testing solvability of max-min interval systems},
     journal = {Kybernetika},
     pages = {879--889},
     year = {2012},
     volume = {48},
     number = {5},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012_48_5_a3/}
}
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Myšková, Helena. An iterative algorithm for testing solvability of max-min interval systems. Kybernetika, Tome 48 (2012) no. 5, pp. 879-889. http://geodesic.mathdoc.fr/item/KYB_2012_48_5_a3/