Abstract In this paper we consider the generalized eigenproblem in max-min (fuzzy) algebra, i.e. given matrices A, B find a vector x and a constant λ such that A x = λ B x where the standard pair of operations, plus and times, have been replaced by the operations maximum and minimum. The entries of the vector or matrix are, in practice, usually not exact numbers and can rather be considered as values in some intervals. In this paper the properties of matrices and vectors with inexact (interval) entries are studied and complete solutions of the strong, the universal, the L-controllable and the R-controllable generalized eigenproblems in max-min (fuzzy) algebra are presented. As a consequence of the obtained results, efficient algorithms for checking all equivalent conditions are introduced.

中文翻译：

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区间最大最小（模糊）矩阵的广义特征问题

摘要 在本文中，我们考虑最大最小（模糊）代数中的广义特征问题，即给定矩阵 A、B 找到向量 x 和常数 λ 使得 A x = λ B x 其中标准操作对，加和倍, 已被操作最大值和最小值取代。在实践中，向量或矩阵的条目通常不是精确的数字，而是可以被视为某些区间中的值。本文研究了具有不精确（区间）项的矩阵和向量的性质，并给出了最大-最小（模糊）代数中强、全能、L-可控和R-可控广义特征问题的完整解。作为获得结果的结果，引入了用于检查所有等效条件的有效算法。