Rank reversal and Rank Preservation in ANP method
Abstract The analytic network process (ANP) as a generalization of the analytic hierarchy process (AHP) can also produce rank reversal phenomenon in multiple criteria decision making (MCDM).The reverse phenomenon can influence the correctness of our decision makers greatly. So the research of rank reversal has great significance in theoretical and practical application. In this paper through the analysis of its calculation process can find that rank reversal is caused by change of ratio among weight values before and after an alternative is added. And use a numerical example to illustrate the rank reversal in the ANP method, look into the cause of that phenomenon and find that rank reversal is caused by change of ratio among weight values before and after an alternative is added. An approach is also proposed based on ideal point to keep the ratio among weight values unchanged to avoid reversal phenomenon and verify the validity of our proposed approach in rank preservation. And we use a numerical instance to verified the approach which can effectively solve the rank reversal problem.