Data analyses by partial order methodology

  • Lars Carlsen Awareness Center, Denmark
Keywords: data analysis, partial ordering, Hasse diagram, indicator importance, peculiar objects, average order, weight regimes, incomparabilities


The present paper reviews data analysis applying partial order methodology. Hence, in addition to a short introduction to the basics of partial ordering a series of central tools of partial order methodology is presented and discussed based on exemplary studies applying a dataset comprising 12 obsolete pesticides characterized by their environmental persistence, bioaccumulation and toxicity.
Partial orders are often visualized by the so-called Hasse diagrams where the characteristics of partial ordering immediately become evident through the structure of the diagrams by levels, chains and antichains. Especially the presence of incomparabilities due to conflicting indicator values calls for attention.
The paper presents tools to a) estimate the relative importance of the single indicators applied, b) disclose the presence of so-called ‘peculiar’ objects that have one or more unexpected high or low indicator values, c) calculate the average order of the single element as partial ordering a priori does not lead to an absolute ordering that often is wanted, d) apply various weighting regimes in order to qualify the ordering, and e) disclose and visualize the actual nature of the incomparabilities that are in inherent part of partial ordering.


1 Annoni P, Bruggemann R, Carlsen L (2015) J Appl Stat 42:535-554.

2 Borken J (2005) Umweltindikatoren als ein Instrument der Technikfolgenabschätzung - Selektion, Aggregation und multikriterielle Bewertung am Beispiel des Verkehrs. Fakultät für Angewandte Wissenschaften. Universität Freiburg/Breisgau. PhD-Thesis, pp. 153.

3 Brans JP, Vincke PH (1985) Manage Sci 31:647-656.

4 Bruggemann R, Annoni P (2014) MATCH Communications in Mathematical and in Computer Chemistry 71:117-142.

5 Bruggemann R, Carlsen L (2006) Partial order in environmental sciences and chemistry, Springer, Berlin, Germany. ISBN 978-3-540-33968-7.

6 Bruggemann R, Carlsen L (2006) Introduction to partial order theory exemplified by the evaluation of sampling sites, In: Partial Order in Environmental Sciences and Chemistry, R. Bruggemann and L. Carlsen, eds, Springer, Berlin. P.61-110. ISBN 978-3-540-33968-7

7 Bruggemann R, Carlsen L (2011) MATCH Communications in Mathematical and in Computer Chemistry 65:383-414.

8 Bruggemann R, Carlsen L (2012) Sci Total Environ 425:293-295.

9 Bruggemann R, Carlsen L (2014) MATCH Communications in Mathematical and in Computer Chemistry 71:694-716.

10   Bruggemann R, Carlsen L (2015) MATCH Communications in Mathematical and in Computer Chemistry 73:277-302

11   Bruggemann R, Carlsen L (2015) MATCH Communications in Mathematical and in Computer Chemistry (Submitted for publication)

12   Bruggemann R, Carlsen L, Voigt K, Wieland R (2014) PyHasse Software for Partial Order Analysis, In: Bruggemann R, Carlsen L, Wittmann J, eds, Multi-Indicator Systems and Modelling in Partial Order. Springer, New York, USA. P.389-423. ISBN 978-1-4614-8223-9

13   Bruggemann R, Halfon E, Welzl G, Voigt K, Steinberg CEW (2001) J Chem Inf Comp Sci 41:918-925.

14   Brüggemann R, Münzer B (1993) Chemosphere 27:1729-1736.

15   Bruggemann R, Patil GP (2011) Ranking and prioritization for multi-indicator systems - Introduction to partial order applications. Springer, New York, USA.

16   Brüggemann R, Restrepo G, Voigt K, Annoni P (2013) MATCH Communications in Mathematical and in Computer Chemistry 69:413-432.

17   Brüggemann R, Sørensen PB, Lerche D, Carlsen L (2004) J Chem Inf Comp Sci 44:618-625.

18   Brüggemann R, Voigt K (1995) Chemosphere 31:3585-3594.

19   Bruggemann R, Voigt K (2011) MATCH Communications in Mathematical and in Computer Chemistry 66:231-251.

20   Carlsen L (2015) AIMS Environm Sci 2:110-121.

21   Carlsen L, Bruggemann R (2015) Partial Ordering and Metrology Analyzing Analytical Performance, Submitted for publication.

22   Colorni A, Paruccini M, Roy B (2001) A-MCD-A, Aide Multi Critere a la Decision, Multiple Criteria Decision Aiding. JRC European Commission, Ispra, Italy.

23   De Loof K, De Meyer H, De Baets B (2006) Fund Inform 71:309-321.

24   European Commission (2006) Regulation No 1907/2006 of the European Parliament and of the Council of 18 December 2006 concerning the Registration, Evaluation, Authorisation and Restriction of Chemicals (REACH), establishing a European Chemicals Agency, amending Directive 1999/45/EC and repealing Council Regulation (EEC) No 793/93 and Commission Regulation (EC) No 1488/94 as well as Council Directive 76/769/EEC and Commission Directives 91/155/EEC, 93/67/EEC, 93/105/EC and 2000/21/EC; Article 57d,e (; Accessed Mar. 2015)

25   Ernesti J, Kaiser P (2008) Python - Das umfassende Handbuch. Galileo Press, Bonn, Germany.

26   Figueira J, Greco S, Ehrgott M (2005) Multiple criteria decision analysis, State of the art surveys. Springer, Boston, USA.

27   Hasse H (1967) Vorlesungen über Klassenkörpertheorie. Physica-Verlag, Marburg, Germany.

28   Hetland ML (2005) Beginning Python - From Novice to professional. Apress, Berkeley, USA.

29   Lerche D, Brüggemann R, Sørensen P, Carlsen L, Nielsen OJ (2002) J Chem Inf Comp Sci 42:1086-1098.

30   Lerche D, Sørensen PB, Brüggemann R (2003) J Chem Inf Comp Sci 43:1471-1480.

31   Morton J, Pachter L, Shiu A, Sturmfels B, Wienand O (2009) Siam J Discrete Math 23:1117-1134.

32   Munda G (2008) Social Multi-Criteria Evaluation for a Sustainable Economy. Springer-Verlag, Berlin, Germany.

33   Python (2015) Python software. (assessed Jan. 2015).

34   R Core Team (2015) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria., ISBN 3-900051-07-0,, (accessed Mar. 2015) (the 3D plot applied the package ‘rgl’).

35   Roy B (1972) Cahiers du Centre d’Etudes de Recherche Operationelle 20:32-43.

36   Roy B, Bouyssou D (1986) Eur J Oper Res 25:200-215.

37   Sailaukhanuly Y, Zhakupbekova A, Amutova F, Carlsen L (2013) Chemosphere 90:112-117.

38   (2008) Stockholm Convention. (accessed Febr. 2015)

39   Sørensen PB, Mogensen BB, Carlsen L, Thomsen M (2000) Chemosphere 41:595-601.

40   Weigend M (2006) Objektorientierte Programmierung mit Python. Mitp-Verlag, Bonn, Germany. ISBN 9783826617508

41   Wienand O (2006) lcell. http// (accessed Feb 2015)


Cited by: 1

1. Carlsen L (2016) An alternative view on distribution keys for the possible relocation of refugees in the European Union. Social Indicators Research. In Press. CrossRef

How to Cite
Carlsen, L. (2015). Data analyses by partial order methodology. Chemical Bulletin of Kazakh National University, 78(2), 22-34.