Eigenvalues and eigenvectors are widely used in various applications. Particularly, these concepts underlie analysis of consistency of a decision maker’s (DMs) preference knowledge. In real-world problems, DMs knowledge is inherently associated with imprecision and partial reliability. This involves combination of fuzzy and probabilistic information. The concept of a Z-number is a formal construct to describe such kind of information. In this study, we formulate the concepts of Z-number valued eigenvalue and eigenvector for matrices components of which are Z-numbers. A formal statement of the problem and a solution method for computation of Z-number valued eigensolutions are proposed. Numerical examples and an application devoted to foreign market selection problem are provided to show the usefulness of the proposed approach.

中文翻译：

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Z数矩阵描述的部分可靠决策偏好的特征解

特征值和特征向量广泛用于各种应用。特别是，这些概念是决策者 (DM) 偏好知识一致性分析的基础。在现实世界的问题中，DM 的知识本质上与不精确性和部分可靠性相关联。这涉及模糊和概率信息的组合。Z 数的概念是描述此类信息的正式结构。在这项研究中，我们制定了 Z 值特征值和特征向量的概念，其中矩阵分量是 Z 数。提出了问题的正式陈述和计算Z值特征解的求解方法。提供了专门针对外国市场选择问题的数值示例和应用程序，以显示所提出方法的有用性。