Preference ranking organization method for enrichment evaluation: Difference between revisions

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Some uses of Promethee and Gaia have become case-studies. Recently these have included:

* Deciding which resources are the best with the available budget to meet SPS quality standards (STDF – [[WTO]]) [See more in External Links]

* Selecting new route for train performance ([[Italferr]])[See more in External Links]

== The mathematical model ==

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:<math>\phi^{-}(a)=\frac{1}{n-1}\displaystyle\sum_{x \in A}\pi(x,a)</math>

The positive preference flow <math>\phi^{+}(a_i)</math> quantifies how a given action <math>a_i</math> is globally preferred to all the other actions while the negative preference flow <math>\phi^{-}(a_i)</math> quantifies how a given action <math>a_i</math> is being globally preferred by all the other actions. An ideal action would have a positive preference flow equal to 1 and a negative preference flow equal to 0. The two preference flows induce two generally different complete rankings on the set of actions. The first one is obtained by ranking the actions according to the decreasing values of their positive flow scores. The second one is obtained by ranking the actions according to the increasing values of their negative flow scores. The Promethee I partial ranking is defined as the intersection of these two rankings. As a consequence, an action <math>a_i</math> will be as good as another action <math>a_j</math> if <math> \phi^{-+}(a_i) \ge \phi^{-+}(a_j)</math> and <math>\phi^{-}(a_i)\le \phi^{-}(a_j)</math>

The positive and negative preference flows are aggregated into the net preference flow:

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* [[Multi-criteria decision analysis]]

* [[Ordinal Priority Approach]]

* [[Pairwise comparison (psychology)|Pairwise comparison]]

* [[Preference]]