A method for multi-attribute decision making based on ER-AHP

As a nascent method of multi-criteria decision-making with uncertainty, DS/AHP is similar to the analytic hierarchy process (AHP) in structure and its analytic processes are based on Dempster-Shafer (DS) theory. However, it is unsuitable to deal with the multi-attribute decision making with incomplete information, especially the attributes with missing values. In this paper, a new method for multiple-attribute decision making based on ER-AHP has been proposed, which incorporates the Evidential Reasoning(ER) algorithm with AHP. Firstly, each alternative is compared with the negative ideal alternative under an attribute to form the decision table by experts. Then a new basic probability assignment function (BPA) is constructed to express the incomplete information and some properties of the function are proved. After then, based on the results of aggregation which combines the attributes of each alternative by the ER algorithm, the alternatives are sorted and selected. Finally, the ER-AHP is compared with the DS / AHP through a numerical example.