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Should the value of the indifference (Q) and preference thresholds (P) be in the interval: min |Dc(Ai,Aj)| <= q <= p <= max |Dc(Ai,Aj)| ? where min |Dc(Ai,Aj)| or max |Dc(Ai,Aj)| is the lowest / the highest deviation value for criterion c? So, it won't make sense if we set Q or P out of the interval. Is that right?
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Author: Bertrand Mareschal
Views: 26
Votes: 11


The values of the Q indifference threshold and of the P preference threshold are linked to the evaluations but also to the preferences of the decision-maker. Often on a quantitative criterion there will be at the same time actions that are very close to each other as well as actions with very different evaluations. Let us note Dmin the minimum (>0) deviation and Dmax the maximum deviation. In such a case, Q will probably be larger than Dmin and P smaller than Dmax. But is is not always the case.

Let us consider for instance criterion Price in the Visual PROMETHEE demo example: Dmin = 500€ and Dmax = 23,000€. Probably (except if you are very rich) Q will be smaller than Dmin and P will be smaller than Dmax.

Let us now consider two possible variants:

  1. Dmin = 5€ and Dmax = 25€. In this case, both Q and P will certainly be larger than Dmax (except if you are very greedy). Actually the criterion is not discriminating the actions, all the prices are very close to each other and the criterion could safely be removed from the analysis (provided you don't change the actions later...).
  2. Dmin = 2,500€ and Dmax = 10,000€. In this case, all the prices are very different from each other and (except if you are very rich) both Q and P will be smaller than Dmin.

As a conclusion, values for Q and P can be based on the distribution of the evaluations (that is to some extent what the Preference Function Assistant of Visual PROMETHEE does) but they should be checked according to how the decision-maker perceives the scale of the criterion.

Last update: 12:45 AM Thursday, May 31, 2012

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