Refining Aggregation Operator-Based Orderings in Multifactorial Evaluation—Part I: Continuous Scales

Aggregation operators are often needed when building preference relations in multicriteria decision making problems. Most existing approaches have limitations due to incomparability between decisions or ties due to the use of some aggregation operations that produce a ranking. The natural way of overcoming the lack of discrimination power is to refine the obtained ranking. We bring an overview of methods that enable aggregation-based rankings to be refined, generalizing concepts like discrimin (max), leximin (max), and Lorentz orderings that refine such aggregation operations like the minimum (the maximum) and the sum.