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AE and EA robustness of interval circulant matrices in max-product algebra

机译：MAX-Product代数中间隔循环矩阵的AE和EA鲁棒性

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Max-product algebra is defined as a linearly ordered set with two binary operations. Classical addition and multiplication are replaced by maximum and multiplication, respectively. A square matrix A is robust, if for each starting vector x, the orbit stabilizes. If this property holds only for starting vectors from an interval vector X, we say that A is X-robust. We shall deal with the matrices of special type: circulant and the corresponding interval version, so-called interval circulant matrices. The interval approach in this paper is applied in combination with for-all-exists quantification of the values - not all of the considered interval matrix entries have the same importance: whereby, for some more important data, all values of the interval must be taken into account and for some less important data it is sufficient to be considered for at least one value of the interval. In this manner, we define the EA and AE robustness and X-robustness of interval circulant matrices over max-product algebra. Polynomial algorithms for checking these types of robustness and X-robustness are presented.(c) 2020 Elsevier B.V. All rights reserved.
机译：Max-Product代数被定义为具有两个二进制操作的线性有序集。经典添加和乘法分别取代了最大和乘法。方形矩阵A是坚固的，如果每个起始载体x，则轨道稳定。如果此属性仅适用于从间隔向量X的启动向量，我们说A是X-FORUST。我们将处理特殊类型的矩阵：循环和相应的间隔版，所谓的间隔循环矩阵。本文中的间隔方法与for-all-aliplys的值相结合应用 - 并非所有考虑的间隔矩阵条目具有相同的重要性：从而为一些更重要的数据，必须采取间隔的所有值考虑到某些不太重要的数据，足以考虑间隔的至少一个值。以这种方式，我们在MAX-Product代数上定义间隔循环矩阵的EA和AE鲁棒性和X稳健性。提供用于检查这些类型的鲁棒性和X稳健性的多项式算法。（c）2020 Elsevier B.v.保留所有权利。

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