Abstract
Various proposals for how to eliminate some of the obstacles in multi-criteria decision making exist and methods for introducing so called surrogate weights have proliferated for some time in the form of ordinal ranking methods for the criteria weights. Considering the decision quality, one main problem is that the input information to ordinal methods is often too restricted. At the same time, decision-makers often possess more background information, for example regarding the relative strengths of the criteria, and might want to use that. Thus, some form of strength relation often exists that can be utilised when transforming orderings into weights. In this article, using a quite extensive simulation approach, we suggest a thorough testing methodology and analyse the relevance of a set of ordering methods including to what extent these improve the efficacy of rank order weights and provide a reasonable base for decision making.
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Notes
- 1.
PA and DR are akin to elements of the SAW approach [8].
- 2.
Sometimes there is a limit to the individual numbers but not a limit to the sum of the numbers.
- 3.
- 4.
We will henceforth, unless otherwise stated, presume that decision problems are modelled as simplexes S w generated by w 1 > w 2 > … > w N , Σw i = 1, and 0 ≤ w i .
- 5.
For example: “A is slightly more important than B while B is vastly more important than C” must, in an ordinal ranking, be expressed as “A is more important than B which is more important than C”.
- 6.
Success measures we used were (a) “winner”, having the same preferred alternative,(b) matching of the three highest ranked alternatives (“podium”), and (c) matching of all ranked alternatives (“overall”), the number of times all evaluated alternatives using a particular method coincide with the true ranking of the alternatives. The two latter sets correlated strongly with the first and are not shown in this paper.
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Acknowledgments
This research was funded by the Swedish Research Council FORMAS, project number 2011-3313-20412-31, as well as by Strategic funds from the Swedish government within ICT – The Next Generation.
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Danielson, M., Ekenberg, L. (2015). Using Surrogate Weights for Handling Preference Strength in Multi-criteria Decisions. In: Kamiński, B., Kersten, G., Szapiro, T. (eds) Outlooks and Insights on Group Decision and Negotiation. GDN 2015. Lecture Notes in Business Information Processing, vol 218. Springer, Cham. https://doi.org/10.1007/978-3-319-19515-5_9
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