Today’s modern decision-making problem is designated by not being the most effective fuzziness; however, additionally partial reliability also plays a crucial role. The incomplete and unreliable information may also affect the selection maker to earn inaccurate decisions, ensuing in monetary losses and wastes of resources. Thus, it is vital to describe the reliability of the facts. To cope with it entirely, a notion of Z-number, i.e., a pair of fuzzy sets modeling a probability-qualified fuzzy statement, is the most suitable medium to access it. In this paper, we spout a new technique to measure the uncertainty of discrete Z-numbers based on Shannon entropy. In the given approach, by using characteristics of Z-number, all the potential probability distributions are estimated by the maximum entropy method. Then, a new fuzzy subset of the Z-number is formed based on the probability distributions and the membership functions of the fuzzy number. Finally, the centroid of the formulated set is determined to rank the degree of the uncertainty of Z-number. The applicability of the delivered approach is read with some numerical examples related to the decision-making process.

中文翻译：

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离散Z值的新不确定性度量

当今的现代决策问题并不是最有效的模糊性。但是，部分可靠性也起着至关重要的作用。不完整和不可靠的信息也可能影响选择者做出错误的决定，从而导致金钱损失和资源浪费。因此，描述事实的可靠性至关重要。为了完全解决它，Z数的概念（即，模拟概率限定的模糊陈述的一对模糊集）是访问它的最合适媒介。在本文中，我们提出了一种基于香农熵的离散Z值不确定性测量新技术。在给定的方法中，利用Z数的特征，通过最大熵方法估计所有潜在概率分布。然后，根据模糊数的概率分布和隶属函数，形成一个新的Z值模糊子集。最后，确定公式集的质心，以对Z值的不确定度进行排序。通过一些与决策过程相关的数字示例来阅读已交付方法的适用性。