Rank reversal in the PROMETHEE II method: Some new results

Bertrand Mareschal · Yves De Smet · Philippe Nemery

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Multi-Criteria Decision Making Game Theory and Voting Systems Optimization and Mathematical Programming

Abstract

The aim of this paper is to study properties of multicriteria decision-aid ranking methods based on pair-wise comparisons in regards to rank reversals. At first we introduce the notion of pair-wise rank reversal and we show that this notion is equivalent to rank reversal. Then we analyze more particularly the PROMETHEE II method and we clarify conditions under which the PROMETHEE II ranking might suffer from rank reversal problems. Finally, we prove that the PROMETHEE multicriteria net flow is the centered score that minimizes the sum of the squared deviations from the pair-wise comparisons of the alternatives.

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References

1983On a short-coming of Saaty's method of analytic hierarchies 1996A note on the use of PROMETHEE multicriteria methods 1998Design and implementation of a group DSS for sustaining renewable energies exploitation 2000Multicriterion Analysis for Sustainable Water Resources Planning: A Case Study in Spain 2001Outranking methods as tools in strategic natural resources planning

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