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Title: Max-min interval systems of linear equations with bounded solution (English)
Author: Myšková, Helena
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 48
Issue: 2
Year: 2012
Pages: 299-308
Summary lang: English
Category: math
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. (English)
Keyword: max-min algebra
Keyword: interval system
Keyword: T6-vector
Keyword: weak T6 solvability
Keyword: strong T6 solvability
Keyword: T7-vector
Keyword: weak T7 solvability
Keyword: strong T7 solvability
MSC: 15A06
MSC: 65G30
idMR: MR2954328
Date available: 2012-05-15T16:19:44Z
Last updated: 2013-09-22
Stable URL:
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