MAX-MIN INTERVAL SYSTEMS OF LINEAR EQUATIONS WITH BOUNDED SOLUTION
Helena Myšková · Czech digital mathematics library · 2012
summary: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.