Skip to main content

Structures of Partial Orders

  • Chapter
  • First Online:
Ranking and Prioritization for Multi-indicator Systems

Part of the book series: Environmental and Ecological Statistics ((ENES))

Abstract

While visualizing a poset (X, IB) with a Hasse diagram, it is initially interesting to observe the following:

1. Whether or not there is a messy system of lines.

2. Whether the Hasse diagram resembles a

a. triangular shape or

b. rectangular shape.

3. Whether there are different components or approximate components.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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.

    We sometimes simplify the notation by omitting the reference to IB’.

References

  • Bruggemann, R., Pudenz, S., Voigt, K., Kaune, A. and Kreimes, K. (1999). An algebraic/graphical tool to compare ecosystems with respect to their pollution. IV: Comparative regional analysis by Boolean arithmetics. Chemosphere, 38(10), 2263–2279.

    Article  Google Scholar 

  • Bruggemann, R. and Voigt, K. (2009). Analysis of partial orders in environmental systems applying the new software PyHasse. In W. Jochen and F. Michael (Eds.), Simulation in Umwelt- und Geowissenschaften, Workshop Potsdam 2009 (pp. 43–55). Aachen: Shaker Verlag.

    Google Scholar 

  • Dutka, B.J., Walsh, K., Kwan, K.K., El Shaarawi, A., Liu, D.L. and Thompson, K. (1986). Priority site selection from degraded areas based on microbial and toxicant screening tests. Water Pollut. Res. J. Can., 21(2), 267–282.

    Google Scholar 

  • Myers, W.L. and Patil, G.P. (2008). Semi-subordination sequences in multi-measure prioritization problems. Chapter 7. In M. Pavan and R. Todeschini (Eds.), Ranking methods: Theory and applications, Data Handling in Science and Technology (pp. 159–168, Vol. 27). Amsterdam, The Netherlands: Elsevier.

    Chapter  Google Scholar 

  • Restrepo, G. and Bruggemann, R. (2008). Dominance and separability in posets, their application to isoelectronic species with equal charge. J. Math. Chem., 44, 577–602.

    Article  MATH  MathSciNet  Google Scholar 

  • Simon, U. (2003). Multikriterielle bewertung von wasserwirtschaftlichen Maβnahmen aus gewaesseroekologischer Sicht – Beispiel Berlin. Berlin: Tenea.

    Google Scholar 

  • Simon, U., Bruggemann, R. and Pudenz, S. (2004a). Aspects of decision support in water management – Example Berlin and Potsdam (Germany) I – Spatially differentiated evaluation. Water Res., 38, 1809–1816.

    Article  Google Scholar 

  • Simon, U., Bruggemann, R. and Pudenz, S. (2004b). Aspects of decision support in water management – Example Berlin and Potsdam (Germany) II – Improvement of management strategies. Water Res., 38, 4085–4092.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rainer Brüggemann .

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Brüggemann, R., Patil, G.P. (2011). Structures of Partial Orders. In: Ranking and Prioritization for Multi-indicator Systems. Environmental and Ecological Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8477-7_5

Download citation

Publish with us

Policies and ethics