Ratio product model: A rank-preserving normalization-agnostic multi-criteria decision-making method

This paper presents a new multi-criteria decision-making (MCDM) method, namely the ratio product model (RPM). We first overview two popular aggregating models: the weighted sum model (WSM) and the weighted product model (WPM). Then, we argue that the two models suffer from some fundamental issues mainly due to ignoring the ratio nature of the alternatives' scores with respect to the criteria and the importance weights of the criteria. Building on the notion of compositional data analysis, the developed RPM regards performance scores and criteria weights as compositions, which solves the issues around the WSM and WPM. Using several examples, we show that the WSM and WPM could lead to erroneous conclusions, whereas the RPM could lead to fully reliable conclusions. Since many MCDM methods rely on some aggregation approaches, the proposed method is a significant contribution to the field and puts forward the correct way to analyze decision problems while respecting the nature and constraints of the input data.

Automated summary

This paper presents a new multi-criteria decision-making method called the ratio product model (RPM) and compares it with the weighted sum model (WSM) and the weighted product model (WPM). The RPM addresses the issues of the WSM and WPM by considering performance scores and criteria weights as compositions. Examples demonstrate that the RPM leads to reliable conclusions while the WSM and WPM may result in erroneous conclusions. The proposed method is a significant contribution to the field of MCDM and provides a correct way to analyze decision problems respecting the nature and constraints of the input data.