Kybernetika 48 no. 2, 299-308, 2012

Max-min interval systems of linear equations with bounded solution

Helena Myšková


Max-min algebra is an algebraic structure in which classical addition and multiplication are replaced by $\oplus$ and $\kr$, where $a\oplus b=\max\{a,b\}, a\kr b=\min\{a,b\}$. The notation $\mbf{A}\kr \mbf{x}=\mbf{b}$ represents an interval system of linear equations, where $\mbf{A}=[\pA,\nA]$, $\mbf{b}=[\pb,\nb]$ are given interval matrix and interval vector, respectively, and a solution is from a given interval vector $\mbf{x}=[\px,\nx]$. We define six types of solvability of max-min interval systems with bounded solution and give necessary and sufficient conditions for them.


max-min algebra, interval system, T6-vector, weak T6 solvability, strong T6 solvability, T7-vector, weak T7 solvability, strong T7 solvability


15A06, 65G30


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