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Published in:
Why Prioritization, Why Ranking Read chapter Read first chapter

2011 | OriginalPaper | Chapter

5. Structures of Partial Orders

Authors : Rainer Brüggemann, Ganapati P. Patil

Published in: Ranking and Prioritization for Multi-indicator Systems

Publisher: Springer New York

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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.

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previous chapter Sensitivity and Ambiguity
next chapter Hasse Diagrams Based on Transformed Data Matrices
Footnotes
1
We sometimes simplify the notation by omitting the reference to IB’.
 
Literature
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.CrossRef
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.
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.
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.CrossRef
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.CrossRefMATHMathSciNet
Simon, U. (2003). Multikriterielle bewertung von wasserwirtschaftlichen Maβnahmen aus gewaesseroekologischer Sicht – Beispiel Berlin. Berlin: Tenea.
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.CrossRef
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.CrossRef
Metadata
Title
Structures of Partial Orders
Authors
Rainer Brüggemann
Ganapati P. Patil
Copyright Year
2011
Publisher
Springer New York
Book
Ranking and Prioritization for Multi-indicator Systems

Print ISBN: 978-1-4419-8476-0

Electronic ISBN: 978-1-4419-8477-7

Copyright Year: 2011

DOI
https://doi.org/10.1007/978-1-4419-8477-7_5

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