Preference ranking organization method for enrichment evaluation: Difference between revisions

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{{Short description|Promethee & Gaia, tools for management}}

{{Use dmy dates|date=AugustDecember 20122021}}

{{multiple issues|

{{COI|date=June 2014}}

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== History==

The basic elements of the Promethee method have been first introduced by Professor Jean-Pierre Brans (CSOO, VUB Vrije Universiteit Brussel) in 1982.<ref name="Brans">{{Cite news|author=J.P. Brans|title=L’ingénierieL'ingénierie de la décision: élaboration d’instrumentsd'instruments d’aided'aide à la décision. La méthode PROMETHEE.|year=1982|publisher=Presses de l’Université Laval}}</ref> It was later developed and implemented by Professor Jean-Pierre Brans and Professor Bertrand Mareschal (Solvay Brussels School of Economics and Management, ULB Université Libre de Bruxelles), including extensions such as GAIA.

The descriptive approach, named Gaia,<ref name="Gaia">{{Cite news|title=Geometrical representations for MCDA. the GAIA module|author1=B. Mareschal |author2=J.P. Brans |year=1988|publisher=European Journal of Operational Research}}</ref> allows the decision maker to visualize the main features of a decision problem: he/she is able to easily identify conflicts or synergies between criteria, to identify clusters of actions and to highlight remarkable performances.

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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>\pi_k(a_i,a_j)=P_k[d_k(a_i,a_j)]</math>

where <math>P_k:\R\rightarrow[0,1]</math> is a positive non-decreasing preference function such that <math>P_jP_k(0)=0</math>. Six different types of preference function are proposed in the original Promethee definition. Among them, the linear unicriterion preference function is often used in practice for quantitative criteria:

:<math>P_k(x) \begin{cases} 0, & \text{if } x\le q_k \\ \frac{x-q_k}{p_k-q_k}, & \text{if } q_k<x\le p_k \\ 1, & \text{if } x>p_k \end{cases}</math>

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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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==See also==

* [[AMIA Systems]]

* [[Decision making]]

* [[Decision-making software]]

* [[D-Sight]]

* [[Multi-criteria decision analysis]]

* [[PairwiseOrdinal comparisonPriority Approach]]

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

* [[Preference]]

==References==

{{Reflist|2reflist}}

==External links==

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* [http://www.promethee-gaia.net PROMETHEE & GAIA web site]

* [http://www.smart-picker.com Smart-Picker Pro implementing PROMETHEE and FLOWSORT]

* [http://en.promethee-gaia.net/assets/vpmanual.pdf User manual for Visual PROMETHEE, a guide to all PROMETHEE methods]

{{DEFAULTSORT:Promethee}}