The purpose of this study is to propose an integrated distance-based methodology for multiple attribute group decision making (MAGDM) within single-valued neutrosophic linguistic (SVNL) environments. A new SVNL distance measure, namely the SVNL integrated weighted distance (SVNLIWD) measure, is first developed for achieving the aim. The remarkable feature of the SVNLIWD is that it integrates both merits of ordered weighting and average weighting into aggregating SVNL distances; therefore, it can account for both the importance of aggregated deviations as well as ordered positions. Thus, it can highlight the decision makers’ subjective risk attitudes and combine the importance of objective decision information. Some distinctive characteristics and special forms of the presented distance framework are then specifically studied. Moreover, a MAGDM model on the basis of the proposed SVNLIWD form is formulated. Finally, an illustrative numerical case regarding selecting low-carbon supplier is used to test the performance of the designed method.

中文翻译：

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单值中智语言集的集成加权距离测度及其在供应商选择中的应用

这项研究的目的是为单值中智语言（SVNL）环境中的多属性组决策（MAGDM）提出一种基于距离的集成方法。为了达到该目的，首先开发了一种新的SVNL距离度量，即SVNL集成加权距离（SVNLIWD）度量。SVNLIWD的显着特征是它将有序加权和平均加权的优点集成到SVNL距离的汇总中。因此，它既可以说明汇总偏差的重要性，也可以说明排序的位置。因此，它可以突出决策者的主观风险态度，并结合客观决策信息的重要性。然后专门研究了所提出的距离框架的一些独特特征和特殊形式。此外，根据所提出的SVNLIWD表格，制定了MAGDM模型。最后，使用关于选择低碳供应商的说明性数值案例来测试设计方法的性能。