Multi-Weight Ranking for Multi-Criteria Decision Making

• URL: http://arxiv.org/abs/2312.03006v2
• Date: Sun, 14 Jan 2024 20:22:12 GMT
• Title: Multi-Weight Ranking for Multi-Criteria Decision Making
• Authors: Andreas H Hamel and Daniel Kostner
• Abstract summary: Cone distribution functions from statistics are turned into Multi-Criteria Decision Making tools. The ranking functions are then extended to providing unary indicators for set preferences. A potential application in machine learning is outlined.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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