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[1] 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.
It has particular application in decision making, and is used around the world in a wide variety of decision scenarios, in fields such as business, governmental institutions, transportation, healthcare and education.
It provides a comprehensive and rational framework for structuring a decision problem, identifying and quantifying its conflicts and synergies, clusters of actions, and highlight the main alternatives and the structured reasoning behind.
The basic elements of the Promethee method have been first introduced by Professor Jean-Pierre Brans (CSOO, VUB Vrije Universiteit Brussel) in 1982.
[2] 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,[3] 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,[4] 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[5] was published in 2010.
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 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:
The applications of Promethee and Gaia to complex multi-criteria decision scenarios have numbered in the thousands, and have produced extensive results in problems involving planning, resource allocation, priority setting, and selection among alternatives.
Other areas have included forecasting, talent selection, and tender analysis.
The basic data related to such a problem can be written in a table containing
Of course, these differences depend on the measurement scales used and are not always easy to compare for the decision maker.
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: where
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.
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.
When a preference function has been associated to each criterion by the decision maker, all comparisons between all pairs of actions can be done for all the criteria.
A multicriteria preference degree is then computed to globally compare every couple of actions: Where
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 positive and negative preference flows are aggregated into the net preference flow: Direct consequences of the previous formula are: The Promethee II complete ranking is obtained by ordering the actions according to the decreasing values of the net flow scores.
It includes preferences, indifferences and incomparabilities (partial preorder).