The information expression and modeling of decision-making are critical problems in the fuzzy decision theory and method. However, existing trapezoidal neutrosophic numbers (TrNNs) and neutrosophic Z-numbers (NZNs) and their multicriteria decision-making (MDM) methods reveal their insufficiencies, such as without considering the reliability measures in TrNN and continuous Z-numbers in NZN. To overcome the insufficiencies, it is necessary that one needs to propose trapezoidal neutrosophic Z-numbers (TrNZNs), their aggregation operations, and an MDM method for solving MDM problems with TrNZN information. Hence, this study first proposes a TrNZN set, some basic operations of TrNZNs, and the score and accuracy functions of TrNZN and their ranking laws. Then, the TrNZN weighted arithmetic averaging (TrNZNWAA) and TrNZN weighted geometric averaging (TrNZNWGA) operators are presented based on the operations of TrNZNs. Next, an MDM approach using the proposed aggregation operators and score and accuracy functions is established to carry out MDM problems under the environment of TrNZNs. In the end, the established MDM approach is applied to an MDM example of software selection for revealing its rationality and efficiency in the setting of TrNZNs. The main advantage of this study is that the established approach not only makes assessment information continuous and reliable but also strengthens the decision rationality and efficiency in the setting of TrNZNs.

中文翻译：

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多准则决策方法及其在梯形中智Z数设定中的应用

决策的信息表达和建模是模糊决策理论和方法中的关键问题。但是，现有的梯形中智数（TrNNs）和中智Z值（NZNs）及其多准则决策（MDM）方法揭示了它们的不足，例如不考虑TrNN中的可靠性指标和NZN中的连续Z值。为了克服这些不足，有必要提出一个梯形的中智Z数（TrNZN），它们的聚合运算以及一种用TrNZN信息解决MDM问题的MDM方法。因此，本研究首先提出了TrNZN集，TrNZN的一些基本操作，TrNZN的得分和准确性函数以及它们的排名定律。然后，基于TrNZN的运算，给出了TrNZN加权算术平均（TrNZNWAA）和TrNZN加权几何平均（TrNZNWGA）运算符。下一个，建立了一种使用提议的聚合算子以及得分和准确性函数的MDM方法，以在TrNZNs环境下解决MDM问题。最后，将已建立的MDM方法应用于软件选择的MDM示例，以揭示其在TrNZN设置中的合理性和效率。这项研究的主要优势在于，既定的方法不仅使评估信息连续且可靠，而且在设置TrNZN时增强了决策的合理性和效率。