Preference ranking organization method for enrichment evaluation: Difference between revisions

Revision as of 11:28, 27 December 2015

Revision as of 05:08, 5 June 2016

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{{technical|date=June 2014}}

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The '''Preference Ranking Organization METHod for Enrichment of Evaluations''' and its descriptive complement '''geometrical analysis for interactive aid''' are better known as the '''Promethee and Gaia'''<ref name="Figueria">{{Cite book|title=Multiple Criteria Decision Analysis: State of the Art Surveys|authorauthor1=J. Figueira, |author2=S. Greco, and |author3=M. Ehrgott |last-author-amp=yes |year=2005|publisher=Springer Verlag }}</ref> methods.

Based on mathematics and sociology, the Promethee and Gaia method was developed at the beginning of the 1980s and has been extensively studied and refined since then.

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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’ingénierie de la décision: élaboration d’instruments d’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|authorauthor1=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.

The prescriptive approach, named Promethee,<ref name="Promethee">{{Cite news|title=A preference ranking organisation method: The PROMETHEE method for MCDM|authorauthor1=J.P. Brans and |author2=P. Vincke |lastauthoramp=yes |publisher=Management Science|year=1985}}</ref> provides the decision maker with both complete and partial rankings of the actions.

Promethee has successfully been used in many decision making contexts worldwide. A non-exhaustive list of scientific publications about extensions, applications and discussions related to the Promethee methods<ref name="applications">{{Cite news|author=M. Behzadian, R.B. Kazemzadeh, A. Albadvi and M. Aghdasi|title=PROMETHEE: A comprehensive literature review on methodologies and applications|year=2010|publisher=European Journal of Operational Research}}</ref> was published in 2010.

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* 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>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>

where <math>q_j</math> and <math>p_j</math> are respectively the indifference and preference thresholds. The meaning of these parameters is the following: when the difference is smaller than the indifference threshold it is considered as negligible by the decision maker. Therefore, the corresponding unicriterion preference degree is equal to zero. If the difference exceeds the preference threshold it is considered to be significant. Therefore, the unicriterion preference degree is equal to one (the maximum value). When the difference is between the two thresholds, an intermediate value is computed for the preference degree using a linear interpolation.

=== Multicriteria preference degree ===

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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:

:<math>\phi(a)=\phi^{+}(a)-\phi^{-}(a)</math>

Direct consequences of the previous formula are:

:<math>\phi(a_i) \in [-1;1]</math>

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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]

{{DEFAULTSORT:Promethee}}

[[Category:Decision theory]]