Incomparable: What Now, IV. Incomparabilities: A Modeling Challenge

  • Rainer Bruggemann
  • Lars Carlsen
  • Paola Annoni


When a mutual ranking of a selection of objects is wanted, an initial step is the development of a multi-indicator system (MIS). Many MCDA concepts, e.g., members of the ELECTRE-family or of the different PROMETHEE versions, are available for obtaining rankings from an MIS. On the one side, a major disadvantage applying these models is the need for additional parameters beyond the data matrix, whereas Partial Order Theory is a methodology that allows extracting ranking information from a data matrix without additional, often subjective and consequently questionable parameters. On the other side, additional parameters help decision-making by introducing knowledge for decision makers/stakeholders beyond the data matrix. The present study focuses on the question to what extent an MIS can be modeled within the framework of partial order theory to add knowledge similarly to the MCDA approaches. Of all the possible alternatives, applying weight intervals to the indicators system is here discussed.


Monte Carlo Partial Order Composite Indicator Weight Combination Weak Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Annoni P, Bruggemann R, Saltelli A (2012) Random and quasi-random designs in variance-based sensitivity analysis for partially ordered sets. Reliab Eng Sys Safety 107:184–189CrossRefGoogle Scholar
  2. Annoni P, Bruggemann R, Carlsen L (2015) A multidimensional view on poverty in the European Union by partial order theory. J Appl Stat 42:535–554CrossRefGoogle Scholar
  3. Bartel H-G, Mucha H-J (2014) Measures of incomparabilities and of inequality and their application. In: Bruggemann R, Carlsen L, Wittmann J (eds) Multi-indicator systems and modelling in partial order. Springer, New York, pp 47–67CrossRefGoogle Scholar
  4. Brans JP, Vincke PH (1985) A preference ranking organisation method (The PROMETHEE Method for Multiple Criteria Decision - Making). Manag Sci 31:647–656CrossRefGoogle Scholar
  5. Bruggemann R, Carlsen L (2012) Multi-criteria decision analyses. Viewing MCDA in terms of both process and aggregation methods: some thoughts, motivated by the paper of Huang, Keisler and Linkov. Sci Total Environ 425:293–295CrossRefGoogle Scholar
  6. Bruggemann R, Carlsen L (2016) An attempt to Understand Noisy Posets. MATCH Commun. Math. Comput. Chem. 75:485–510Google Scholar
  7. Bruggemann R, Patil GP (2011) Ranking and prioritization for multi-indicator systems - introduction to partial order applications. Springer, New YorkCrossRefGoogle Scholar
  8. Bruggemann R, Voigt K (2012) Antichains in partial order, example: pollution in a German region by Lead, Cadmium Zinc and Sulfur in the herb layer. MATCH Commun Math Comput Chem 67:731–744Google Scholar
  9. Bruggemann R, Voigt K, Restrepo G, Simon U (2008) The concept of stability fields and hot spots in ranking of environmental chemicals. Environ Model Softw 23:1000–1012CrossRefGoogle Scholar
  10. Bruggemann R, Kerber A, Restrepo G (2011) Ranking objects using fuzzy orders, with an application to refrigerants. MATCH Commun Math Comput Chem 66:581–603Google Scholar
  11. Bruggemann R, Restrepo G, Voigt K, Annoni P (2013) Weighting intervals and ranking. Exemplified by leaching potential of pesticides. MATCH Commun Math Comput Chem 69:413–432Google Scholar
  12. Bruggemann R, Carlsen L, Voigt K, Wieland R (2014) PyHasse software for partial order analysis: scientific background and description of selected modules. In: Bruggemann R, Carlsen L, Wittmann J (eds) Multi-indicator systems and modelling in partial order. Springer, New York, pp 389–423CrossRefGoogle Scholar
  13. Carlsen L (2008) Hierarchical partial order ranking. Environ Pollut 155:247–253CrossRefGoogle Scholar
  14. Carlsen L, Bruggemann R (2014) The ‘Failed Nations Index’ offers more than just a simple ranking. Soc Indic Res 115:525–530CrossRefGoogle Scholar
  15. Carlsen L, Bruggemann R (2016) On the influence of data noise and uncertainty on ordering of objects, described by a multi-indicator system. A set of pesticides as an exemplary case. J Chemom 30(1):22–29CrossRefGoogle Scholar
  16. Carlsen L, Bruggemann R, Kenessova O, Erzhigitov E (2015) Evaluation of analytical performance based on partial order methodology. Talanta 132:285–293CrossRefGoogle Scholar
  17. Gomes LFAM, Rangel LAD (2009) An application of the TODIM method to the multicriteria rental evaluation of residential properties. Eur J Oper Res 193:204–211CrossRefGoogle Scholar
  18. Kerber A, Bruggemann R (2015) Problem driven evaluation of chemical compounds and its exploration. Match Commun Math Comput Chem 73:577–618Google Scholar
  19. Munda G (2008) Social multi-criteria evaluation for a sustainable economy. Springer, BerlinCrossRefGoogle Scholar
  20. Peters ML, Zelewski S (2007) TOPSIS als technik zur effizienzanalyse. WiSt Jnuar 2007:9–15CrossRefGoogle Scholar
  21. Roy B (1990) The outranking approach and the foundations of the ELECTRE methods. In: Bana e Costa CA (ed) Readings in multiple criteria decision aid. Springer, Berlin, pp 155–183CrossRefGoogle Scholar
  22. Sailaukhanuly Y, Zhakupbekova A, Amutova F, Carlsen L (2013) On the ranking of chemicals based on their PBT characteristics: comparison of different ranking methodologies using selected POPs as an illustrative example. Chemosphere 90:112–117CrossRefGoogle Scholar
  23. Wieland R, Bruggemann R (2013) Hasse diagram technique and Monte Carlo simulations. MATCH Commun Math Comput Chem 70:45–59Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of EcohydrologyLeibniz—Institute of Freshwater Ecology and Inland FisheriesBerlinGermany
  2. 2.Awareness CenterRoskildeDenmark
  3. 3.Economic Analysis UnitEuropean Commission-Directorate General for Regional and Urban PolicyBrusselsBelgium

Personalised recommendations