The concept of Z‐number, is very new in the literature, proposed by Zadeh in 2011. The Z‐number Z = ( A , B ) is a pair of fuzzy numbers where the first component represents the restriction and the second component represents the certainty of the first component. Further, its application is evident in decision‐making problems, risk assessment, linear programming problems, and so forth. Hence, under such circumstances ranking of Z‐numbers need an utmost attention, as such, a few methods of ranking Z‐numbers are proposed by various researcher. However, in many situations the existing methods depict drawbacks and limitations as discussed in this paper. Hence, a new method of ranking Z‐numbers is essential for an appropriate decision‐making. In this paper, a new method of ranking Z‐numbers based on the concept of value and ambiguity at levels of decision‐making have been proposed. The method seems to deliver a reasonable decision and proper ranking of Z‐numbers of various types. A few numerical examples are discussed which show the out‐performance of the proposed method.

中文翻译：

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基于决策级别的价值和歧义的 Z 数排名

Z-number 的概念在文献中是非常新的，由 Zadeh 在 2011 年提出。 Z-number Z = ( A , B ) 是一对模糊数，其中第一个分量表示限制，第二个分量表示第一部分的确定性。此外，它在决策问题、风险评估、线性规划问题等方面的应用也很明显。因此，在这种情况下，Z-number 的排序需要高度关注，因此，各种研究人员提出了一些 Z-number 排序方法。然而，在许多情况下，现有方法描述了本文中讨论的缺点和局限性。因此，一种对 Z 数进行排序的新方法对于适当的决策至关重要。在本文中，提出了一种基于价值概念和决策级别模糊性对 Z 数进行排序的新方法。该方法似乎提供了各种类型的 Z 数的合理决策和适当排序。讨论了一些数值例子，显示了所提出方法的优异性能。