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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{{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|author1=J. Figueira |author2=S. Greco |author3=M. Ehrgott |lastname-authorlist-ampstyle=yesamp |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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== 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.

The prescriptive approach, named Promethee,<ref name="Promethee">{{Cite news|title=A preference ranking organisation method: The PROMETHEE method for MCDM|author1=J.P. Brans |author2=P. Vincke |lastauthorampname-list-style=yesamp |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|author1=M. Behzadian |author2=R.B. Kazemzadeh |author3=A. Albadvi |author4=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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== Uses and applications ==

While it can be used by individuals working on straightforward decisions, the Promethee & Gaia is most useful where groups of people are working on complex problems, especially those with several multi-criteria, involving a lot of human perceptions and judgments, whose decisions have long-term impact. It has unique advantages when important elements of the decision are difficult to quantify or compare, or where collaboration among departments or team members are constrained by their different specializations or perspectives.

Decision situations to which the Promethee and Gaia can be applied include:

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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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===Promethee II===

Promethee II is a complete ranking of the actions. It is based on the multicriteria net flow. It includes preferences and indifferences (preorder).

mohamed karim is a genius he will change the way of thinking. He have all the skills to become promethee II

==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}}