A new approach for multi-attribute decision making problem with incomplete information based on Dempster-Shafer theory

In this paper, for the multi-attribute decision making problems with incomplete information, a new approach is proposed based on the Dempster-Shafer theory, which has simple decision rule and could solve a problem directly based on its incomplete decision matrix. First identify all possible focal elements from the incomplete decision matrix, and then calculate the basic probability assignment of each focal element and the belief function of each decision alternative. Preference relations among the alternatives are determined by their belief functions. A numerical example is given to illustrate the detailed implementation process of the new approach.