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.