To overcome the insufficiencies of existing information expression and operations of single-valued neutrosophic multisets (SVNMs) and multi-valued/hesitant neutrosophic sets (MVNSs), this study first introduces neutrosophic multi-valued sets (NMVSs), including SVNMs and MVNSs, as a general concept. Then, we propose a method that transforms NMVSs into consistency single-valued neutrosophic sets (CSVNSs) based on the average values and consistency degrees (complement of standard deviations) of the truth, indeterminacy, falsity multi-valued sequences in NMVSs. CSVNSs not only can realize the reasonable information expression and operation of different sequence lengths/cardinalities between neutrosophic multi-valued elements, but also can reflect the multi-valued sequences close to corresponding average levels in each neutrosophic multi-valued element. Next, we present two correlation coefficients between CSVNSs in the setting of NMVSs. Based on the correlation coefficients of CSVNSs, a decision-making (DM) approach is established in the NMVS setting. Lastly, an illustrative example and comparison with existing methods are presented to demonstrate the effectiveness and rationality of the established DM method in the NMVS setting. The developed DM approach not only makes the DM process more reasonable and credible, but also provides the new modeling method for multi-attribute DM problems in NMVS setting.

为了克服现有的信息表达和单值中智多值集（SVNM）和多值/止血中智集（MVNS）的不足，本研究首先介绍了中智多值集（NMVS），包括SVNM和MVNS。一个一般的概念。然后，我们提出了一种基于NMVS的真值，不确定性，虚假多值序列的平均值和一致性程度（标准偏差的补充），将NMVS转换为一致性单值中智集（CSVNS）的方法。CSVNSs不仅可以实现中智多值元素之间不同序列长度/基数的合理信息表达和运算，而且可以反映每个中智多值元素中接近相应平均水平的多值序列。接下来，我们在NMVS的设置中给出CSVNS之间的两个相关系数。基于CSVNS的相关系数，在NMVS设置中建立了决策（DM）方法。最后，给出了一个示例性例子并与现有方法进行了比较，以证明已建立的DM方法在NMVS环境中的有效性和合理性。发达的DM方法不仅使DM过程更加合理和可信，而且为NMVS设置中的多属性DM问题提供了新的建模方法。给出了一个说明性示例，并与现有方法进行了比较，以证明已建立的DM方法在NMVS环境中的有效性和合理性。发达的DM方法不仅使DM过程更加合理和可信，而且为NMVS设置中的多属性DM问题提供了新的建模方法。给出了一个说明性示例，并与现有方法进行了比较，以证明已建立的DM方法在NMVS环境中的有效性和合理性。发达的DM方法不仅使DM过程更加合理和可信，而且为NMVS设置中的多属性DM问题提供了新的建模方法。