Outranking Methods - PROMETHEE

Extended Version


The method called Preference Ranking Organisation Method for Enrichment Evaluations (PROMETHEE) was developed by Brans (1982), further extended by Brans and Vincke (1985) and Brans and Mareschal (1994). It is an outranking method, typical of the European (or French) MCA school.

Outranking methods are characterized by the limited degree to which a disadvantage on a particular viewpoint may be compensated by advantages on other viewpoints (Pirlot, 1997). The degree of dominance of one option over another is indicated by outranking (Vincke, 1992). PROMETHEE is a well-established decision support system which deals with the appraisal and selection of a set of options on the basis of several criteria, with the objective of identifying the pros and the cons of the alternatives and obtaining a ranking among them.


With PROMETHEE, as an outranking method, strong assumptions concerning the ‘true’ preference structure of the decision maker are avoided. In the evaluation of decision alternatives, the key question is whether thereis enough information to state that one alternative is at least as good as another. On the basis of so−called outranking relations, which are build in a first step, a ranking of alternatives is derived from.

In the following lines, we give an overview of the principles of the PROMETHEE approach (For detailed calculation steps please check the corresponding literature, e.g. Brans and Vincke 1985).


  1. Assigning a preference function:
  • The starting point is the evaluation matrix, which presents the performance of each alternative in relation to each criterion. Using the data contained in the evaluation matrix, the alternatives are compared pairwise with respect to every single criterion. The results are expressed by the preference functions, which are calculated for each pair of options and can range from 0 to 1. Whereas 0 means that there is no difference between the pair of options, 1 indicates a big difference.
  1. Estimating the outranking degree of the options:
  • By multiplying the preferences by the criteria’s weights and adding the single values, a matrix of global preferences is calculated. In this matrix, the sum of the row expresses the strength of an alternative (dominance). The sum of the column expresses how much an alternative is dominated by the other ones (subdominance). A linear ranking is obtained by subtracting the subdominance−value from the dominance−value (Simon et al., 2001).


Decision makers are required to weigh criteria and to choose a preference function. Promethee does not provide specific guidelines for determining weights to criteria, but assumes that the decision maker is able to weigh the criteria appropriately, at least when the number of criteria is not too large (Macharis et al., 2004). Each ‘weighing’ remains subjective and is restricted only to the evaluated alternatives. Therefore, sensitivity analyses, which clarify how far the chosen weights influence the output, become important (Geldermann and Rentz, 1999).

Various PROMETHEE tools and modules have been developed so far. For analysing an evaluation problem, the following three main Promethee tools can be especially used:

  • PROMETHEE I for partial ranking,
  • PROMETHEE II for complete ranking and
  • GAIA plane for visualisation.

PROMETHEE I provides a partial preorder of alternatives, which, in some cases, may be incomplete. This means that some alternatives cannot be compared and, therefore, cannot be included in complete ranking. This occurs when the one alternative obtains high scores on particular criteria for which another alternative obtains low scores and the opposite occurs between the same alternatives for other criteria. The use of PROMETHEE I then suggests that the decision maker should engage in additional evaluation efforts (Macharis et al., 2004). The advantage of the partial preorder is that some bad performing alternatives can be excluded from the further evaluation exercises, with the consequence that the data requirement is reduced (Geldermann and Rentz, 1999).

PROMETHEE II provides a complete ranking of alternatives from the best to the worst one. As explained in the first chapter, when dealing with sustainability issues, it is more useful to present a ranking of options than a single solution. In this sense, it is useful to supply to the decision maker information on how the final ranking changes when different decisions on weights, criteria and aggregation procedures are taken (Kangas et al. 2001).


Evaluation of results

Policy processes:

PROMETHEE can help exploring weak and strong points of policy options. It delivers a ranking of options which facilitates the selection of a policy option, and in a participative context also supports the social debate. PROMETHEE can be used in the stage of recognizing and investigating the nature of a problem only to a limited extend, since it cannot really structure a decision problem. It delivers a ranking of options which facilitates the selection of a policy option, but it is less suitable for the implementation and the evaluation of an implemented policy.

Sustainability aspects:

PROMETHEE is capable to compare long−term impacts, independently of the gauge year. Further sustainability aspects such as, (de−)coupling, adaptability, (ir−)reversibility can be incorporated as criteria to compare alternative policies. Also the impacts on distributional effects over different groups/sectors/regions can be included in PROMETHEE as separate categories. PROMETHEE can compare impacts independently of the global dimension and can be applied to spatial data. Environmental, economic and social impacts can be covered by PROMETHEE, even simultaneously. This feature is very useful because when dealing with sustainability, some impacts cannot be expressed in quantitative terms.

Operational aspects:

Manpower and time needs as well as the costs for applying the tool are difficult to estimate and depend highly on the subject. The same holds for data needs and data availability. In general, as it is the case with other MCA, a lot of data is needed to estimate the impacts. In addition, the required amount of expert judgement to explain the results can be high. Qualitative and quantitative data can be dealt with simultaneously, and data can be used in their own units.

The ways in which the preference information is processed are rather complicated and hard to explain to non−experts. Comprehension of the method and the interpretability of the results can be difficult, which can be the main shortcomings of most outranking methods from the viewpoint of their practical application. Nevertheless, in general, the transparency of PROMETHEE is rather high.

Ranking irregularities can occur when a new alternative is introduced. But sensitivity analysis allows the decision maker to assess how alternative ratings would change if criteria weights were changed. The ability to deal with uncertain and fuzzy information is a clear−cut advantage of PROMETHEE (as of outranking methods). No specific time scale is associated with the application of PROMETHEE and there are no limitations regarding the geographical coverage.


Mladineo et al. (1987) applied the PROMETHEE method for the ranking of alternative locations for small scale hydro plants and found this method appropriate in the planning period of problem solving when there are neither sufficient data nor financial means for its realization. The main objective of the analysis (in this phase of problem solving) was the selection of the best locations to be further analysed, and to estimate their economic efficiency within a given period of time.

Briggs et al. (1990) analyzed with PROMETHEE and GAIA a problem related to nuclear waste management. A quite large number of scenarios were envisaged, which had to be assessed against a small number of strongly conflicting criteria. They showed how GAIA and PROMETHEE can help to choose among alternative policy options, respectively by describing them and supporting the decision− making process.

With the objective to develop a set of tools designed to guide forest manager's decisions in a manner that will improve forest sustainability Waaub et al. (2000) applied PROMETHEE to compare strategic planning forest scenarios in Quebec, Canada.

A group decision making procedure based on PROMETHEE (Brans, Macharis and Mareschal, 1997) was elaborated and tested in the context of watershed management (Martin, St−Onge and Waaub, 1997). The approach was used in a process of negotiation in a collaborative environment and facilitated the participation of stakeholders.

Hermans and Erickson (2004) reported from two case studies in the Northeastern United States, where

management options for forest and water resources were evaluated, and in a third case, land use change and policy options were addressed. In each case, PROMETHEE was used to aid stakeholders in negotiating compromises and in reaching operational decisions.

PROMETHEE as one of the presented MCA methods was not applied during the case study of Sustainability−A−Test. With regard to the topic of the case study, the Biofuels Directive and the Energy Crop Premium, PROMETHEE could have been used to support the stages of policy options description and evaluation as well as the selection of a policy option by providing a ranking of options.


PROMETHEE has been combined with Geographic Information Systems (GIS) and spatial models for land use suitability assessment and sustainable forest management. PROMETHEE can be used to compare the impact of alternative policies generated by other tools like physical assessment tools, modelling tools and environmental appraisal tools. PROMETHEE can also be used in combination with stakeholder analyses and is capable to support the evaluation of alternative policies/plans/projects in policy impact assessment and SEA.

Strengths and weaknesses


  • PROMETHEE supports group−level decision making because it constitutes a useful platform for debate and consensus building.
  • PROMETHEE (as all outranking methods) can simultaneously deal with qualitative and quantitative criteria. Criteria scores can be expressed in their own units
  • PROMETHEE can deal with uncertain and fuzzy information.


  • PROMETHEE suffers from the rank reversal problem when a new alternative is introduced (De Keyser and Peeter, 1996).
  • PROMETHEE does not provide the possibility to really structure a decision problem. In the case of many criteria and options, it thus may become difficult for the decision maker to obtain a clear view of the problem and to evaluate the results.
  • Until now, PROMETHEE does not provide any formal guidelines for weighing, but assumes that the decision maker is able to weigh the criteria appropriately. Therefore, a new approach was suggested by Macharis et al. (2004) which replicates the AHP weighing approach in a PROMETHEE context.
  • The way in which the preference information is processed is complicated and hard to explain to non−specialists.

Further work

Within the range of reported PROMETHEE−applications, EU examples are still rare. It might be interesting to use PROMETHEE to compare alternative European policies. Another interesting direction is to combine PROMETHEE with other MCA methods.


Bouyssou, D., Vincke, Ph., 1997: Ranking Alternatives on the Basis of Preference Relations: A Progress Report with Special Emphasis on Outranking Relations. Journal of Multi−Criteria Decision Analysis, 6, 77−85.

Brans, J.P., Macharis, C., Mareschal, B., 1997: The GDSS Promethee. Vrije Universiteit Brussel, STOOTW/277.

De Keyser, W., Peeters, P., 1996: A note on the use of Promethee multicriteria methods. European Journal of Operational Research, 89: 457−461.

Hermans, C. and Erickson, J., 2004: Regional Land use planning decisions on watershed scale: practical experiences in MCDA from three case studies. MCDM 2004, Whistler, B.C., Canada.

Kangas, J., Kangas, A., Leskinen, P., Pykäläinen, J., 2001: MCDM Methods in Strategic Planning of Forestry on state−owned lands in Finland: Applications and Experiences. Journal of Multi−Criteria Decision Analysis, 10: 257−271.

Macharis, C., Springael J., De Brucker, K., Verbeke, A., 2004: PROMETHEE and AHP: The design of operational synergies in multicriteria analysis. Strengthening PROMETHEE with ideas of AHP. European Journal of Operational Research 153: 307−317.

Office of the Deputy Prime Minister (ODPM, Government UK), 2004: DTLR multi−criteria analysis manual. Corporate Publication. Internet: http://www.communities.gov.uk/index.asp?id=1142251

Pirlot, M. 1997: A Common Framework for Describing Some Outranking Methods. Journal of Multi−Criteria Decision Analysis, 6: 86−92.