Information reliability has a remarkable effect on decision-making outcome. Zadeh’s Z-number considers information fuzziness and reliability, and can, therefore, help the decision-maker to manage complicated problems. However, due to its complex construct, several issues concerning the computation of Z-numbers require further research. This study develops a novel likelihood-based method of comparing two Z-numbers to solve multi-criteria decision-making (MCDM) problems. Four main parts can be outlined. First, the likelihood of fuzzy restriction of Z-numbers is defined based on the conversion method of Z-number. Second, the likelihood of underlying probability distributions of Z-numbers is also proposed to compare the difference of randomness of Z-information. Third, by adding to a risk preference parameter, this study constructs a comprehensive weighted likelihood of Z-numbers. Finally, a likelihood-based qualitative flexible approach is extended to address the MCDM problems under Z-evaluation. In addition, a numerical example of the selection of ERP systems for ABC enterprise is placed to illustrate the applicability, validity, and effectiveness of the proposed method.

中文翻译：

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基于可能性的定性灵活方法对决策问题中的Z数进行排名

信息可靠性对决策结果有显着影响。Zadeh的Z数考虑了信息的模糊性和可靠性，因此可以帮助决策者管理复杂的问题。但是，由于其复杂的构造，有关Z数计算的几个问题需要进一步研究。这项研究开发了一种新颖的基于可能性的比较两个Z值的方法，以解决多准则决策（MCDM）问题。可以概述四个主要部分。首先，模糊限制的可能性ž -值是基于所述转换方法定义ž -number。第二，Z的潜在概率分布的可能性还提出了使用-个数来比较Z信息的随机性差异。第三，通过添加风险偏好参数，本研究构建了Z值的综合加权似然性。最后，扩展了一种基于似然性的定性灵活方法，以解决Z评估下的MCDM问题。另外，通过算例对ABC企业选择ERP系统进行了数值模拟，以说明该方法的适用性，有效性和有效性。