Multi-Weight Ranking for Multi-Criteria Decision Making
This work addresses decision-making challenges in optimization and AI by providing a novel scalarization method, though it appears incremental in extending existing statistical concepts to new domains.
The paper tackles the problem of multi-criteria decision making by converting cone distribution functions into ranking tools, which generalizes weighted sum scalarizations to handle multiple weightings simultaneously and detect non-convex Pareto frontiers. It also extends these functions to sets, linking set optimization with multi-objective optimization for potential machine learning applications.
Cone distribution functions from statistics are turned into Multi-Criteria Decision Making tools. It is demonstrated that this procedure can be considered as an upgrade of the weighted sum scalarization insofar as it absorbs a whole collection of weighted sum scalarizations at once instead of fixing a particular one in advance. As examples show, this type of scalarization--in contrast to a pure weighted sum scalarization-is also able to detect ``non-convex" parts of the Pareto frontier. Situations are characterized in which different types of rank reversal occur, and it is explained why this might even be useful for analyzing the ranking procedure. The ranking functions are then extended to sets providing unary indicators for set preferences which establishes, for the first time, the link between set optimization methods and set-based multi-objective optimization. A potential application in machine learning is outlined.