Reducing the Number of Incomparabilities

  • Rainer Brüggemann
  • Ganapati P. Patil
Part of the Environmental and Ecological Statistics book series (ENES)


In Chapter 6, we have shown as to how we can obtain simpler Hasse diagrams from messy ones. We transformed the data matrix so that incomparabilities or comparabilities disappear because objects become equivalent.


Partial Order Data Matrix Linear Order Weighting Scheme Linear Extension 
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. Bruggemann, R., Restrepo, G. and Voigt, K. (2008). Towards a new and advanced partial order program: PyHasse. In J. Owsinski and R. Bruggemann (Eds.), Multicriteria ordering and ranking: Partial orders, ambiguities and applied issues (pp. 11–33). Warsaw: Systems Research Institute Polish Academy of Sciences.Google Scholar
  2. Carlsen, L. and Bruggemann, R. (2009). Partial order ranking as a tool in environmental impact assessment. PAH and PCB pollution of the river main as an illustrative example. In G.T. Halley and Y.T. Fridian (Eds.), Environmental impact assessment (pp. 335–354). Hauppauge, NY: Nova Science Publishers.Google Scholar
  3. Carlsson, C. and Fuller, R. (2002). Fuzzy reasoning in decision making and optimization. Heidelberg: Physica-Verlag.CrossRefMATHGoogle Scholar
  4. Munda, G. (2008). Social multi-criteria evaluation for a sustainable economy (pp. 1–210). Berlin: Springer.CrossRefGoogle Scholar
  5. Myers, W.L., Patil, G.P. and Cai, Y. (2006). Exploring patterns of habitat diversity across landscapes using partial ordering. In R. Bruggemann and L. Carlsen (Eds.), Partial order in environmental sciences and chemistry (pp. 309–325). Berlin: Springer.CrossRefGoogle Scholar
  6. OECD (Nardo, M., et al.). (2008). Handbook on constructing composite indicators – methodology and user guide (pp. 1–158). Ispra: OECD.Google Scholar
  7. Patil, G.P. (2005). Cross-disciplinary class room notes. Center for Statistical Ecology and Environmental Statistics, Penn State University.Google Scholar
  8. Restrepo, G., Bruggemann, R., Weckert, M., Gerstmann, S. and Frank, H. (2008). Ranking patterns, an application to refrigerants. Match – Commun. Math. Comput. Chem., 59, 555–584.MATHMathSciNetGoogle Scholar
  9. Simon, U., Brüggemann, R., Behrendt, H., Shulenberger, E. and Pudenz, S. (2006). METEOR: A step-by-step procedure to explore effects of indicator aggregation in multi criteria decision aiding – Application to water management in Berlin, Germany. Acta Hydrochim. Hydrobiol., 34, 126–136.CrossRefGoogle Scholar
  10. Simon, U., Bruggemann, R., Mey, S. and Pudenz, S. (2005). METEOR – Application of a decision support tool based on discrete mathematics. Match – Commun. Math. Comput. Chem., 54(3), 623–642.Google Scholar
  11. Voigt, K. and Bruggemann, R. (2008). Ranking of pharmaceuticals detected in the environment: Aggregation and weighting procedures. Comb. Chem. High Throughput Screen., 11, 770–782.CrossRefGoogle Scholar
  12. Yager, R.R. (1993). Families of OWA operators. Fuzzy Sets Syst., 59, 125–148.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of EcohydrologyLeibniz Institute of Freshwater Ecology and Inland FisheriesSchöneicheGermany
  2. 2.Center for Statistical Ecology and Environmental StatisticsPennsylvania State UniversityUniversity ParkUSA

Personalised recommendations