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Keywords:
max-plus algebra; interval system; T4 vector; T4 solvability
max-plus algebra; interval system; T4 vector; T4 solvability
Summary:
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.
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