The theory of D numbers (DNs) is an extension of Dempster–Shafer (D–S) evidence theory. Linguistic DNs (LDNs) combine the advantages of the linguistic terms (LTs) and DNs, and can express the uncertain and incomplete information more easily and precisely in decision-making. In addition, the Bonferroni mean (BM) operator and the TOPSIS method are both useful tools to address multiple-attribute group decision-making (MAGDM) problems. Then, in this paper, we extend the BM operator based on the new defined operational rules of LDNs to propose the linguistic D number arithmetic Bonferroni mean (LDABM) operator and the linguistic D number weighted arithmetic Bonferroni mean (LDWABM) operator. We also integrate the proposed LDWABM operator and the TOPSIS method, and further establish a novel method to address MAGDM problems. Finally, we use the proposed method to solve the practical problems of investment decision-making and materials supplier selection and then we prove the feasibility and the superiority of the proposed method by comparing with other methods.

中文翻译：

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基于语言D数的多准则群体决策问题的新方法

D数（DNs）理论是Dempster–Shafer（D–S）证据理论的扩展。语言DN（LDN）结合了语言术语（LT）和DN的优点，并且可以在决策过程中更轻松，更准确地表达不确定和不完整的信息。另外，Bonferroni均值（BM）运算符和TOPSIS方法都是解决多属性小组决策（MAGDM）问题的有用工具。然后，在本文中，我们根据新定义的LDN操作规则扩展BM算子，以提出语言D数算术Bonferroni均值（LDABM）算子和语言D数加权算术Bonferroni均数（LDWABM）算子。我们还将提出的LDWABM算子和TOPSIS方法进行了集成，并进一步建立了解决MAGDM问题的新方法。最后，