Real-world decision-making is based on human cognitive information, which is characterized by fuzziness and partial reliability. In order to better describe such information, Zadeh proposed the concept of Z-number. Ranking the Z-number is an indispensable step in solving the decision-making problem under the Z-number-based information. Golden rule representative value is a new concept introduced by Yager to rank interval values. This article expands it and proposes a new golden rule representative value for fuzzy numbers, and then, apply it to the ranking of the Z-number. Some new rules involving the centroid and fuzziness of fuzzy numbers are constructed to capture the preference of decision-makers. The Takagi–Sugeno–Kang fuzzy model is used to implement these rules. The obtained Rep function is used to construct a new golden rule representative value fuzzy subset of the Z-number and associate this new fuzzy subset with a scalar value. This fuzzy subset not only implies the fuzzy aspect of the Z-number but also contains the information in the hidden probability distribution. The scalar value is regarded as the golden rule representative value of the Z-number to participate in the ranking. The proposed method greatly retains the original information of the Z-number and can overcome the shortcomings of the existing methods. Some numerical examples are used to describe the specific process of the proposed method. The comparative analysis and discussion with existing methods clarify the advantages of the proposed method.

中文翻译：

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基于已开发的黄金法则代表值的 Z 编号排名

现实世界的决策是基于人类的认知信息，具有模糊性和部分可靠性的特点。为了更好地描述此类信息，Zadeh 提出了 Z-number 的概念。对 Z-number 进行排序是解决基于 Z-number 信息下的决策问题必不可少的步骤。Golden rule representative value 是 Yager 引入的对区间值进行排序的新概念。本文对其进行扩展，提出了一种新的模糊数黄金法则代表值，并将其应用于Z数的排序。构建了一些涉及模糊数的质心和模糊性的新规则来捕捉决策者的偏好。Takagi–Sugeno–Kang 模糊模型用于实施这些规则。得到的Rep函数用来构造一个新的Z数的黄金法则代表值模糊子集，并将这个新的模糊子集与一个标量值相关联。这个模糊子集不仅暗示了 Z 数的模糊方面，而且还包含隐藏概率分布中的信息。标量值作为Z数的黄金法则代表值参与排名。所提方法极大地保留了Z-number的原始信息，克服了现有方法的不足。一些数值例子被用来描述所提出方法的具体过程。与现有方法的比较分析和讨论阐明了所提出方法的优点。这个模糊子集不仅暗示了 Z 数的模糊方面，而且还包含隐藏概率分布中的信息。标量值作为Z数的黄金法则代表值参与排名。所提方法极大地保留了Z-number的原始信息，克服了现有方法的不足。一些数值例子被用来描述所提出方法的具体过程。与现有方法的比较分析和讨论阐明了所提出方法的优点。这个模糊子集不仅暗示了 Z 数的模糊方面，而且还包含隐藏概率分布中的信息。标量值作为Z数的黄金法则代表值参与排名。所提方法极大地保留了Z-number的原始信息，克服了现有方法的不足。一些数值例子被用来描述所提出方法的具体过程。与现有方法的比较分析和讨论阐明了所提出方法的优点。所提方法极大地保留了Z-number的原始信息，克服了现有方法的不足。一些数值例子被用来描述所提出方法的具体过程。与现有方法的比较分析和讨论阐明了所提出方法的优点。所提方法极大地保留了Z-number的原始信息，克服了现有方法的不足。一些数值例子被用来描述所提出方法的具体过程。与现有方法的比较分析和讨论阐明了所提出方法的优点。