Skip to main content

Beyond Multicriteria Ranking Problems: The Case of PROMETHEE

  • Chapter
  • First Online:
New Perspectives in Multiple Criteria Decision Making

Part of the book series: Multiple Criteria Decision Making ((MCDM))

Abstract

PROMETHEE is a well-known multicriteria outranking method. If it was primarily developed for (complete or partial) ranking purposes, recent extensions have been proposed in sorting and clustering contexts. Among them, the methods called PROMETHEE TRI and PROMETHEE CLUSTER were first presented in 2004. Unfortunately, these suffered from some drawbacks that we highlight in this contribution. To overcome these problems, authors have developed other extensions such as FlowSort, PCLUST, etc. The purpose of this paper is to provide a summary of some of these contributions, to highlight their existing links and list several remaining research questions. From a global perspective, we will show that the boundaries between ranking, sorting and clustering are blurred.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Preference Ranking Organization Method for Enrichment Evaluations.

  2. 2.

    Graphical Analysis for Interactive Assistance.

References

  • Behzadian, M., Kazemzadeh, R. B., Albadvi, A., & Aghdasi, M. (2010). Promethee: A comprehensive literature review on methodologies and applications. European Journal of Operational Research, 200(1), 198–215.

    Article  Google Scholar 

  • Belacel, N. (2000). Multicriteria assignment method PROAFTN: Methodology and medical application. European Journal of Operational Research, 125(1), 175–183.

    Article  Google Scholar 

  • Boujelben, M. A. (2017). A unicriterion analysis based on the promethee principles for multicriteria ordered clustering. Omega, 69(Supplement C), 126–140.

    Article  Google Scholar 

  • Boujelben, M. A., & De Smet, Y. (2016). A multicriteria ordered clustering algorithm to determine precise or disjunctive partitions. International Journal of Multicriteria Decision Making, 6(2), 157–187.

    Article  Google Scholar 

  • Bouyssou, D., & Perny, P. (1992). Ranking methods for valued preference relations: A characterization of a method based on leaving and entering flows. European Journal of Operational Research, 61(1), 186–194. IFORS-SPC Conference on Decision Support Systems.

    Article  Google Scholar 

  • Brans, J. P., & Mareschal, B. (1992). PROMETHEE V: MCDM problems with segmentation constraints. INFOR: Information Systems and Operational Research, 30(2), 85–96.

    Google Scholar 

  • Brans, J.-P., & Mareschal, B. (1994). The promcalc & gaia decision support system for multicriteria decision aid. Decision Support Systems, 12(4), 297–310.

    Article  Google Scholar 

  • Cailloux, O., Lamboray, C., & Nemery, P. (2007). A taxonomy of clustering procedures. In 66th Meeting of the European Working Group on MCDA (p. N/A), Marrakech, Morocco

    Google Scholar 

  • Calders, T., & Van Assche, D. (2018). PROMETHEE is not quadratic: An o(qnlog(n)) algorithm. Omega, 76(Supplement C), 63–69.

    Google Scholar 

  • Campos, A. C. S. M., Mareschal, B., & de Almeida, A. T. (2015). Fuzzy flowsort: An integration of the flowsort method and fuzzy set theory for decision making on the basis of inaccurate quantitative data. Information Sciences, 293(Supplement C), 115–124.

    Google Scholar 

  • Doan, N. A. V., & De Smet, Y. (2016, December). On the use of reference profiles to compute alternative PROMETHEE II rankings: A preliminary study. In 2016 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM) (pp. 326–330)

    Google Scholar 

  • Doumpos, M., & Zopounidis, C. (2002). Multicriteria Decision Aid Classification Methods (Vol. 73). Applied Optimization. Boston: Springer, Formerly Kluwer Academic Publishers.

    Google Scholar 

  • Duda, R. O., Hart, P. E., & Stork, D. G. (2000). Pattern Classification (2nd ed.). New York: Wiley-Interscience.

    Google Scholar 

  • Dunn, J. C. (1974). Well-separated clusters and optimal fuzzy partitions. Journal of Cybernetics, 4(1), 95–104.

    Article  Google Scholar 

  • Eppe, S., Roland, J., & De Smet, Y. (2014). On the use of valued action profiles for relational multi-criteria clustering. International Journal of Multicriteria Decision Making, 4(3), 201–233. PMID: 64796.

    Article  Google Scholar 

  • Eppe, S., & De Smet, Y. (2017). On the influence of altering the action set on PROMETHEE ii’s relative ranks. In Proceedings of Evolutionary Multi-Criterion Optimization - 9th International Conference, EMO 2017, Münster, Germany, March 19–22, 2017 (pp. 206–220).

    Google Scholar 

  • Fernandez, E., Navarro, J., & Bernal, S. (2010). Handling multicriteria preferences in cluster analysis. European Journal of Operational Research, 202(3), 819–827.

    Article  Google Scholar 

  • Figueira, J., De Smet, Y., & Brans, J. P. (2004). MCDA methods for sorting and clustering problems: Promethee TRI and promethee CLUSTER. Technical report TR/SMG/2004-002, SMG, Université Libre de Bruxelles.

    Google Scholar 

  • Hayez, Q., De Smet, Y., & Bonney, J. (2012). D-sight: A new decision making software to address multi-criteria problems. International Journal of Decision Support System Technology (IJDSST), 4(4), 1–23.

    Article  Google Scholar 

  • Janssen, P., & Nemery, P. (2013). An extension of the flowsort sorting method to deal with imprecision. 4OR, 11(2):171–193.

    Google Scholar 

  • De Keyser, W., & Peeters, P. (1996). A note on the use of promethee multicriteria methods. European Journal of Operational Research, 89(3), 457–461.

    Article  Google Scholar 

  • Köksalan, M., Mousseau, V., & Özpeynirci, S. (2017). Multi-criteria sorting with category size restrictions. International Journal of Information Technology & Decision Making, 16(01), 5–23.

    Article  Google Scholar 

  • Larichev, O., & Moshkovich, H. (1994). An approach to ordinal classification problems. International Transactions in Operational Research, 1(3), 375–385.

    Article  Google Scholar 

  • Liu, Y., Xindong, W., & Shen, Y.-D. (2011). Automatic clustering using genetic algorithms. Applied Mathematics and Computation, 218(4), 1267–1279.

    Article  Google Scholar 

  • Lolli, F., Ishizaka, A., Gamberini, R., Rimini, B., & Messori, M. (2015). Flowsort-gdss a novel group multi-criteria decision support system for sorting problems with application to fmea. Expert Systems with Applications, 42(17), 6342–6349.

    Article  Google Scholar 

  • Mareschal, B., De Smet, Y., & Nemery, P. (2008, December). Rank reversal in the promethee ii method: Some new results. In 2008 IEEE International Conference on Industrial Engineering and Engineering Management (pp. 959–963).

    Google Scholar 

  • Massaglia, R., & Ostanello, A. (1991). N-TOMIC: A support system for multicriteria segmentation problems. In P. Korhonen, A. Lewandowski, & J. Wallenius (Eds.), Multiple Criteria Decision Support: Proceedings, Helsinki, Finland, 1989 (Vol. 356, pp. 167–174). Lectures Notes in Economics and Mathematical Systems. Berlin: Springer.

    Google Scholar 

  • Meyer, P., & Olteanu, A.-L. (2013). Formalizing and solving the problem of clustering in mcda. European Journal of Operational Research, 227(3), 494–502.

    Article  Google Scholar 

  • Moscarola, J., & Roy, B. (1977). Procédure automatique d’examen de dossiers fondée sur une segmentation trichotomique en présence de critères multiples. R.A.I.R.O. Recherche Opérationnelle/Operations Research, 11(2), 145–173.

    Google Scholar 

  • Nemery, P., & Lamboray, C. (2008). Flowsort: A flow-based sorting method with limiting or central profiles. TOP, 16(1), 90–113.

    Article  Google Scholar 

  • Nemery De Bellevaux, P. (2008, November). On the use of multicriteria ranking methods in sorting problems. Ph.D. thesis, Université libre de Bruxelles, Brussels, Belgium.

    Google Scholar 

  • Rocha, C., Dias, L. C., & Dimas, I. (2013). Multicriteria classification with unknown categories: A clustering-sorting approach and an application to conflict management. Journal of Multi-criteria Decision Analysis, 20(1–2), 13–27.

    Article  Google Scholar 

  • Roland, J., De Smet, Y., & Verly, C. (2012). Rank reversal as a source of uncertainty and manipulation in the PROMETHEE II ranking: A first investigation. In Advances in Computational Intelligence - 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, Catania, Italy, July 9–13, 2012, Proceedings, Part IV (pp. 338–346).

    Google Scholar 

  • Rolland, A. (2013). Reference-based preferences aggregation procedures in multi-criteria decision making. European Journal of Operational Research, 225(3), 479–486.

    Article  Google Scholar 

  • Rosenfeld, J., & De Smet, Y. (2017). An extension of promethee to hierarchical multicriteria clustering. Technical report TR/SMG/2017-001, SMG, Université Libre de Bruxelles.

    Google Scholar 

  • Roy, B. (1996). Multicriteria Methodology for Decision Aiding. Dordrecht: Kluwer Academic.

    Book  Google Scholar 

  • Sarrazin, R., De Smet, Y., & Rosenfeld, J. (2018). An extension of promethee to interval clustering. Omega, 80, 12–21.

    Google Scholar 

  • De Smet, Y. (2014, December). An extension of promethee to divisive hierarchical multicriteria clustering. In 2014 IEEE International Conference on Industrial Engineering and Engineering Management (pp. 555–558).

    Google Scholar 

  • De Smet, Y., & Guzmàn, L. M. (2004). Towards multicriteria clustering: An extension of the k-means algorithm. European Journal of Operational Research, 158(2), 390–398. Methodological Foundations of Multi-criteria Decision Making.

    Article  Google Scholar 

  • De Smet, Y., Hubinont, J. P., & Rosenfeld, J. (2017). A note on the detection of outliers in a binary outranking relation. In Proceedings of Evolutionary Multi-Criterion Optimization - 9th International Conference, EMO 2017, Münster, Germany, March 19–22, 2017 (pp. 151–159).

    Google Scholar 

  • De Smet, Y., Nemery, P., & Selvaraj, R. (2012). An exact algorithm for the multicriteria ordered clustering problem. Omega, 40(6), 861–869. Special Issue on Forecasting in Management Science.

    Google Scholar 

  • Sobrie, O. (2016, June). Learning preferences with multiple-criteria models. Ph.D. thesis, Université de Mons (Faculté Polytechnique) and Université Paris-Saclay (CentraleSupélec).

    Google Scholar 

  • Van Assche, D., & De Smet, Y. (2016). Flowsort parameters elicitation based on categorisation examples. International Journal of Multicriteria Decision Making, 6(3), 191–210.

    Article  Google Scholar 

  • Verly, C., & De Smet, Y. (2013). Some results about rank reversal instances in the promethee methods. International Journal of Multicriteria Decision Making, 3(4), 325–345.

    Article  Google Scholar 

  • Vincke, P. (1992). Multicriteria Decision-Aid. New York: Wiley.

    Google Scholar 

  • Yu, W. (1992). Aide Multicritère à la Décision dans le Cadre de la Problématique du Tri : Concepts. Méthodes et Applications. Thèse de Doctorat: LAMSADE, Université Paris Dauphine, Paris, France.

    Google Scholar 

  • Zopounidis, C., & Doumpos, M. (2002). Multicriteria classification and sorting methods: A literature review. European Journal of Operational Research, 138(2), 229–246.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yves De Smet .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

De Smet, Y. (2019). Beyond Multicriteria Ranking Problems: The Case of PROMETHEE. In: Doumpos, M., Figueira, J., Greco, S., Zopounidis, C. (eds) New Perspectives in Multiple Criteria Decision Making. Multiple Criteria Decision Making. Springer, Cham. https://doi.org/10.1007/978-3-030-11482-4_3

Download citation

Publish with us

Policies and ethics