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Keywords:
max-min algebra; interval system; T4-vector; T4 solvability; T5-vector; T5 solvability
max-min algebra; interval system; T4-vector; T4 solvability; T5-vector; T5 solvability
Summary:
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.
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