Systems working in discrete time (discrete event systems, in short: DES)—based on binary operations: the maximum and the minimum—are studied in so-called max–min (fuzzy) algebra. The steady states of a DES correspond to eigenvectors of its transition matrix. In reality, the matrix (vector) entries are usually not exact numbers and they can instead be considered as values in some intervals. The aim of this paper is to investigate the eigenvectors for max–min matrices (vectors) with interval coefficients. This topic is closely related to the research of fuzzy DES in which the entries of state vectors and transition matrices are kept between 0 and 1, in order to describe uncertain and vague values. Such approach has many various applications, especially for decision-making support in biomedical research. On the other side, the interval data obtained as a result of impreciseness, or data errors, play important role in practise, and allow to model similar concepts. The interval approach in this paper is applied in combination with forall–exists quantification of the values. It is assumed that the set of indices is divided into two disjoint subsets: the E-indices correspond to those components of a DES, in which the existence of one entry in the assigned interval is only required, while the A-indices correspond to the universal quantifier, where all entries in the corresponding interval must be considered. In this paper, the properties of EA/AE-interval eigenvectors have been studied and characterized by equivalent conditions. Furthermore, numerical recognition algorithms working in polynomial time have been described. Finally, the results are illustrated by numerical examples.

中文翻译：

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间隔最大-最小矩阵的EA / AE特征向量

在离散时间下工作的系统（离散事件系统，简称为DES）-基于二进制运算：最大值和最小值-在所谓的max-min（模糊）代数中进行了研究。DES的稳态对应于其过渡矩阵的特征向量。实际上，矩阵（向量）条目通常不是精确的数字，而是可以将它们视为某些间隔中的值。本文的目的是研究具有间隔系数的最大最小矩阵（向量）的特征向量。该主题与模糊DES的研究紧密相关，在模糊DES中，状态向量和过渡矩阵的项保持在0和1之间，以描述不确定和模糊的值。这种方法有许多应用，特别是在生物医学研究中的决策支持上。另一方面，由于不精确或数据错误而获得的区间数据在实践中起着重要作用，并且可以对相似的概念进行建模。本文中的区间方法与值的永久存在量化结合使用。假定索引集分为两个不相交的子集：E索引对应于DES的那些组件，其中仅需要在指定间隔中存在一个条目，而A索引对应于DES的那些。通用量词，必须考虑相应间隔中的所有条目。本文研究了EA / AE区间特征向量的性质，并通过等价条件对其进行了表征。此外，已经描述了在多项式时间内工作的数值识别算法。最后，