Weighted power-weakness ratio for multi-criteria decision making

This work presents the weighted power-weakness ratio (wPWR), a multivariate index for multi-criteria decision-making (MCDM) and ranking comparison. The index derives from the power-weakness ratio (PWR) originally proposed to select the strongest winner of tournaments, which has been re-adapted in this study to solve MCDM problems. Key features of wPWR are: (1) its multivariate character, (2) the ability to account simultaneously for the strengths and weaknesses of each element, (3) the possibility to weight criteria according to previous knowledge about the problem. In order to analyze wPWR, we selected three datasets available in scientific literature. The obtained wPWR scores and rankings were compared with four well-established techniques: Simple Average Ranking, Dominance, Reciprocal Rank Fusion and Kendall-Wei approach. Where rankings obtained by other techniques were available from literature, they were also included in the analysis. Results highlighted a correct correlation between wPWR and the other ranking measures, but also interesting differences that support its introduction in the field of MCDM and chemometrics.