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A hitchhiker's guide to poset ranking
Karel De Loof1, Bernard De Baets, Hans De Meyer
1Department of Applied Mathematics and Computer Science, Ghent University, Gent, Belgium. Karel.DeLoof@ugent.be
Combinatorial Chemistry & High Throughput Screening
|November 11, 2008
Summary
Ranking objects using multicriteria analysis is challenging due to differing scales. Partially ordered sets (posets) offer a robust alternative for ranking without common scales, providing a valuable framework for complex decision-making.
Area of Science:
- Decision Sciences
- Operations Research
- Computer Science
Background:
- Multicriteria analysis often requires subjective scaling or weighting of criteria, leading to controversial rankings.
- Traditional ranking methods struggle with incomparable criteria, necessitating artificial constraints.
Purpose of the Study:
- To provide a comprehensive literature review on ranking objects using partially ordered sets (posets).
- To formalize the object ranking problem within a theoretical framework.
- To demonstrate the practical application and effectiveness of poset-based algorithms.
Main Methods:
- Formalization of the object ranking problem with multiple criteria.
- Review and illustration of various algorithms based on partially ordered sets.
- Application of algorithms to a toy example and a real-world scenario.
Main Results:
- Partially ordered sets provide a formal framework for ranking objects without requiring common scales or weights.
- Algorithms based on posets offer a viable alternative to traditional multicriteria analysis.
- Real-world application demonstrates the practical utility of poset-based ranking.
Conclusions:
- Poset theory offers a mathematically sound and practical approach to multicriteria object ranking.
- This method avoids the limitations of traditional approaches by not imposing artificial constraints.
- The study highlights the power of poset-based algorithms in handling complex ranking scenarios.
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