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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Notes
- 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.
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.
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.
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.
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.
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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
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