A novel approach to multi-criteria group decision-making problems based on linguistic D numbers

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.