Sensitivity analysis of the parameters for preference functions and rank reversal analysis in the PROMETHEE II method

The PROMETHEE II method is a classical multiple criteria decision making method. However, it also exists the rank reversal which is a highly important problem for analyzing the reliability of a MCDM method. The main objective of this study is to analyze the sensitivity of the parameters for preference functions and the rank reversal problem in the PROMETHEE II method. By analyzing the parameters for preference functions from the standpoint of theoretics, a method is proposed to calculate the ranges of the parameters for four types of preference functions to remain the ranking of all the alternatives unchanged. Second, the sufficient and necessary condition of the rank reversal is obtained in the PROMETHEE II method when there are only three types of criteria, i.e., usual criteria, $U$-shape criteria and level criteria. Finally, two minor modification methods for the PROMETHEE II method itself are proposed by observing the net outranking flow formula. Numerical simulations show that the occurrence of the rank reversal is clearly reduced and the ranges of fault tolerance of the parameters for preference functions are significantly larger for each new modified PROMETHEE II method. The similarity of rankings is tested by using the similarity rank coefficient $WS$. This indicates the rationality of the two proposed modifications.