Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Posets (books)
Brüggemann R, Drescher-Kaden U (2003) Einführung in die modellgestützte Bewertung von Umweltchemikalien-Datenabschätzung, Ausbreitung, Verhalten, Wirkung und Bewertung. 1 Ed. Springer-Verlag, Berlin
Davey BA, Priestley HA (1990) Introduction to Lattices and Order. Cambridge University Press, Cambridge
Erné M (1982) Einführung in die Ordnungstheorie. BI Wissenschaftsverlag Mannheim
Neggers J, Kim HS (1998) Basic Posets. Singapore: World Scientific Publishing Co
Schröder BSW (2003) Ordered Sets-An Introduction. Birkhäuser, Boston
Trotter WT (1991) Combinatorics and Partially Ordered Sets Dimension Theory; John Hopkins Series in the Mathematical Science. The J Hopkins University Press: Baltimore
Posets as tools for data exploration
Brüggemann R, Altschuh J (1991) A validation study for the estimation of aqueous solubility from n-octanol/water partition coefficients. Sci Tot Environ 109/110:41–57
Brüggemann R, Bartel HG (1999) A Theoretical Concept to Rank Environmentally Significant Chemicals. J Chem Inf Comput Sci 39:211–217
Brüggemann R, Bücherl C, Pudenz S, Steinberg C (1999) Application of the concept of Partial Order on Comparative Evaluation of Environmental Chemicals. Acta hydrochim hydrobiol 27:170–178
Brüggemann R, Halfon E (1990) Ranking for Environmental Hazard of the Chemicals Spilled in the Sandoz Accident in November 1986. Sci Tot Environ 97/98:827–837
Brüggemann R, Halfon E (1997) Comparative Analysis of Nearshore Contaminated Sites in Lake Ontario: Ranking for Environmental Hazard. J Environ Sci Health A32(1):277–292
Brüggemann R, Halfon E, Welzl G, Voigt K, Steinberg C (2001) Applying the Concept of Partially Ordered Sets on the Ranking of Near-Shore Sediments by a Battery of Tests. J Chem Inf Comp Sc 41:918–925
Brüggemann R, Münzer B (1993) A Graph-Theoretical Tool for Priority Setting of Chemicals. Chemosphere 27:1729–1736
Brüggemann R, Münzer B, Halfon E (1994) An Algebraic/Graphical Tool to Compare Ecosystems with Respect to their Pollution-The German River “Elbe” as an Example-I: Hasse-Diagrams. Chemosphere 28:863–872
Brüggemann R, Oberemm A, Steinberg C (1997) Ranking of Aquatic Effect Tests Using Hasse Diagrams. Toxicological and Environmental Chemistry 63:125–139
Brüggemann R, Pudenz S, Voigt K, Kaune A, Kreimes K (1999) An algebraic/graphical tool to compare ecosystems with respect to their pollution. IV: Comparative regional analysis by Boolean arithmetics. Chemosphere 38:2263–2279
Brüggemann R, Schwaiger J, Negele RD (1995) Applying Hasse Diagram Technique for the evaluation of toxicological fish tests. Chemosphere 30(9):1767–1780
Brüggemann R, Zelles L, Bai QY, Hartmann A (1995) Use of Hasse Diagram Technique for Evaluation of Phospholipid Fatty Acids Distribution in Selected Soils. Chemosphere 30(7):1209–1228
Halfon E (1989) Comparison of an index function and a vectorial approach method for ranking waste disposal sites. Environ Science Technol 23:600–609
Halfon E and Brüggemann R (1989) Environmental hazard ranking of chemicals spilled in the Rhine River in November 1986. Acta hydrochim hydrobiol 17:47–60
Halfon E, Reggiani MG (1986) On Ranking Chemicals for Environmental Hazard. Environ Science Technol 20:1173–1179
Helm D (2003) Bewertung von Monitoringdaten der Umweltprobenbank des Bundes mit der Hasse-Diagramm-Technik. UWSF — Z Umweltchem Ökotox 15:85–94
Lorenz R, Brüggemann R, Steinberg C, Spieser OH (1996) Humic Material Changes effects of Terbutylazine on Behavior of Zebrafish (Brachydanio Rerio). Chemosphere 33(11):2145–2158
Münzer B, Brüggemann R, Halfon E (1994) An Algebraic/Graphical Tool to Compare Ecosystems with Respect to their Pollution II: Comparative Regional Analysis. Chemosphere 28:873–879
Patil GP, Taillie C (2005) Multiple indicators, partially ordered sets, and linear extensions: Multi-criterion ranking and prioritization. Environmental and Ecological Statistics 11:199–228
Schrenk C, Pflugmacher S, Brüggemann R, Sandermann HJ, Steinberg C, Kettrup A (1998) Glutathione S-Transferase Activity in Aquatic Macrophytes with Emphasis on Habitat Dependence. Ecotox Environ Saf 40:226–233
Voigt K, Gasteiger J, Brüggemann R (2000) Comparative Evaluation of Chemical and Environmental Online and CD-ROM Databases. J Chem Inf Comp Sc 40:44–49
Voigt K, Welzl G (2002) Chemical databases: an overview of selected databases and evaluation methods. Online Information Review 26:172–192
Voigt K, Welzl G, Brüggemann R (2004) Data analysis of environmental air pollutant monitoring systems in Europe. Environmetrics 15:577–596
Voigt K, Welzl G, Brüggemann R, Pudenz S (2002) Bewertungsansatz von Umweltmonitoring-Informationssystemen in Ballungsräumen. UWSF — Z Umweltchem Ökotox 14:58–64
Posets as tools to chemical investigations
Altschuh J, Brüggemann R, Behrendt H, Münzer B (1996) Relationship between Environmental Fate and Chemical Structure of Solvents. In: Gasteiger, J (Ed.) Software-Entwicklung in der Chemie 10. Gesellschaft Deutscher Chemiker, Frankfurt, pp 105–116
Babic D, Trinajstic N (1996) Möbius inversion on a poset of a graph and its acyclic subgraphs. Discrete Appl Math 67:5–11
Brüggemann R, Pudenz S, Carlsen L, Sørensen PB, Thomsen M, Mishra RK (2001) The Use of Hasse Diagrams as a Potential Approach for Inverse QSAR. SAR and QSAR Environ Res 11:473–487
Carlsen L, Lerche DB, Sørensen PB (2002) Improving the Predicting Power of Partial Order Based QSARs through Linear Extensions. J Chem Inf Comp Sc 42:806–811
Carlsen L, Sørensen PB, Thomsen M (2000) Estimation of Octanol-Water Distribution coefficients-using partial order technique. In: Sørensen PB et al. (Eds.) Order Theoretical Tools in Environmental Sciences-Proceedings of the Second Workshop, October 21st, 1999 in Roskilde, Denmark, 1 Ed. National Environmental Research Institute, Roskilde, pp 105–115
Carlsen L, Sørensen PB, Thomsen M (2001) Partial Order Ranking-based QSAR’s: estimation of solubilities and octanol-water partitioning. Chemosphere 43:295–302
Carlsen L, Sørensen PB, Thomsen M, Brüggemann R (2002) QSAR’s based on Partial Order Ranking. SAR and QSAR in Environmental Research 13:153–165
El-Basil S, Shalabi AS (1985) On the ordering of Kekulé Structures, spectral moments of factor graphs of benzenoid hydrocarbons. Match Commun Math Comput Chem 17:11–43
Pavan M (2003) Total and Partial Ranking Methods in Chemical Sciences. 1–277. 2003. University of Milan — Bicocca, Cycle XVI, Tutor: Prof. Todeschini. Ref Type: Thesis/Dissertation
Pudenz S, Brüggemann R, Bartel HG (2002) QSAR of Ecotoxicological Data on the Basis of Data-Driven If-Then-Rules. Ecotoxicology 11:337–342
RandiĆ M (1990) The nature of chemical structure. J Math Chem 4:157–184
RandiĆ M (2002) On Use of Partial Ordering in Chemical Applications. In: Voigt K and Welzl G (Eds.) Order Theoretical Tools in Environmental Sciences-Order Theory (Hasse Diagram Technique) Meets Multivariate Statistics. Shaker-Verlag, Aachen, pp 55–64
Ruch E, Gutman I (1979) The Branching Extent of Graphs. J of Combinatorics-Inform System Sciences 4:285–295
Posets and Multicriteria Decision Analysis
Colorni A, Paruccini M, Roy B (2001) A-MCD-A, Aide Multi Critere a la Decision, Multiple Criteria Decision Aiding. JRC European Commission, Ispra
Heinrich R (2001) Leitfaden Wasser-Nachhaltige Wasserwirtschaft; Ein Weg zur Entscheidungsfindung. Wasserforschung e.V. Berlin
Lerche D, Brüggemann R, Sørensen PB, Carlsen L, Nielsen OJ (2002) A Comparison of Partial Order Technique with three Methods of Multicriteria Analysis for Ranking of Chemical Substances. J Chem Inf Comp Sc 42:1086–1098
Pudenz S, Brüggemann R (2002) A New Decision Support System: METEOR. In: Voigt K and Welzl G (Eds.) Order Theoretical Tools in Environmental Sciences-Order Theory (Hasse Diagram Technique) Meets Multivariate Statistics. Shaker-Verlag, Aachen, pp 103–112
Roy B (1972) Electre III: Un Algorithme de Classements fonde sur une representation floue des Preferences En Presence de Criteres Multiples. Cahiers du Centre d’Etudes de Recherche Operationelle 20:32–43
Roy B (1980) Selektieren, Sortieren und Ordnen mit Hilfe von Prävalenzrelationen: Neue Ansätze auf dem Gebiet der Entscheidungshilfe für Multikriteria-Probleme. zfbf-Schmalenbachs Zeitschrift für betriebswirtschaftliche Forschung 32:465–497
Roy B (1990) The outranking approach and the foundations of the ELECTRE methods. In: Bana e Costa (Ed.) Readings in Multiple Criteria Decision Aid. Springer-Verlag Berlin, pp 155–183
Simon U, Brüggemann R and Pudenz S (2004) Aspects of decision support in water management-example Berlin and Potsdam (Germany) II-improvement of management strategies. Wat Res 38:4085–4092
Simon U, Brüggemann R, and Pudenz S (2004) Aspects of decision support in water management-example Berlin and Potsdam (Germany) I-spatially differentiated evaluation. Wat Res 38:1809–1816
Simon U, Brüggemann R, Mey S, Pudenz S (2005) METEOR-application of a decision support tool based on discrete mathematics. Match Commun Math Comput Chem 54(3):623–642
Posets and Linear extensions
Atkinson MD (1989) The complexity of Orders. In: Rival, I (Ed.) Algorithms and Order NATO ASI series, Series C. Mathematical and Physical Sciences, Vol 255, Kluwer Academic Publishers, Dordrecht, pp 195–230
Brüggemann R (2004) Lokale partielle Ordnungen, ein Hilfsmittel für die Bewertung? In: Wittmann J and Wieland R (Eds.) Simulation in Umwelt-und Geowissenschaften-Workshop Müncheberg 2004. Shaker-Verlag Aachen, pp 109–123
Brüggemann R, Simon U, Mey S (2005) Estimation of averaged ranks by extended local partial order models. Match Commun Math Comput Chem 54(3):489–518
Brüggemann R, Sørensen PB, Lerche D, Carlsen L (2004) Estimation of Averaged Ranks by a Local Partial Order Model. J Chem Inf Comp Sc 44:618–625
Lerche D, Sørensen PB (2003) Evaluation of the ranking probabilities for partial orders based on random linear extensions. Chemosphere 53:981–992
Lerche D, Sørensen PB, Brüggemann R (2003) Improved Estimation of the Ranking Probabilities in Partial Orders Using Random Linear Extensions by Approximation of the Mutual Probability. J Chem Inf Comp Sc 53:1471–1480
Sørensen PB et al. (2003) Probability approach applied for prioritisation using multiple criteria-Cases: Pesticides and GIS. In: Sørensen PB et al. (Eds.) Order Theory in Environmental Sciences-Integrative approaches, Proceedings of the 5th workshop held at NERI, 2002. NERI, Ministry of the Environment, Denmark, Roskilde, pp 121–136
Sørensen PB, Lerche D (2002) Quantification of the uncertainty Related to the Use of a Limited Number of Random Linear Extensions. In: Voigt K and Welzl G (Eds.) Order Theoretical Tools in Environmental Sciences-Order Theory (Hasse Diagram Technique) Meets Multivariate Statistics. Shaker-Verlag Aachen, pp 65–72
Winkler P (1982) Average height in a partially ordered set. Discr Math 39:337–341
Posac
Borg I, Shye S (1995) Facet Theory-Form and Content. Sage Publications, Thousand Oaks, California
Brüggemann R, Welzl G and Voigt K (2003) Order Theoretical Tools for the Evaluation of Complex Regional Pollution Patterns. J Chem Inf Comp Sc 43:1771–1779
Shye S (1985) Multiple Scaling-The theory and application of partial order scalogram analysis. North-Holland, Amsterdam
Systat Program http://www.spss.com/software/science/SYSTAT/, SPSS Inc., 2000
Formal Concept Analysis
Bartel HG and John PE (1999) Formalbegriffsanalytische Untersuchung von Struktur-Eigenschafts-Beziehungen an Stannaocanen und Stannatranen unter Verwendung von 119 Sn-NMR-Daten. Zeitschr für physikalische Chemie 209:141–158
Bartel HG and Brüggemann R (1998) Application of formal concept analysis to structure-activity relationships. Fresenius J Anal Chem 361:23–28
Bartel HG (1995) Formale Begriffsanalyse und Materialkunde: Zur Archäometrie altägyptischer glasartiger Produkte. Match Commun Math Comput Chem 32:27–46
Bartel HG (1996) Mathematische Methoden in der Chemie. Spektrum Akademischer Verlag, Oxford, pp 1–353
Bartel HG (1997) Ein neuer Ansatz zur formalbegriffsanalytischen Objektklassifikation und seine Anwendung auf aromatische Heterocyclische Verbindungen. Match Commun Math Comput Chem 36:185–215
Bartel HG (1998) Formal Concept Analysis in Ecotoxicology. In: Group Pragmatic Theoretical Ecology (Ed.), Proceedings of the Workshop on Order Theoretical Tools in Environmental Sciences Berichte des IGB, Heft 6, Sonderheft I, 1998, IGB, Berlin, pp 111–117
Bartel HG (2000) Formal Concept Analysis and Chemometrics: Chemical Composition of Ancient Egyptian Bronze artifacts. Match Commun Math Comput Chem 42:25–38
Ganter B and Wille R (1986) Implikationen und Abhängigkeiten zwischen Merkmalen. In: Degens PO, Hermes HJ and Opitz O (Eds.) Die Klassifikation und ihr Umfeld. Indeks-Verlag Frankfurt, pp 171–185
Ganter B and Wille R (1996) Formale Begriffsanalyse Mathematische Grundlagen, Springer-Verlag Berlin, pp 1–286
Ganter B and Wille R (1996) Formale Begriffsanalyse Mathematische Grundlagen, Springer-Verlag Berlin, pp 1–286
Kerber A (2005) Posets and Lattices, Contexts and Concepts. Match Commun Math Comput Chem 54(3):551–560
Wille R (1996) Allgemeine Mathematik, Mathematik für die Allgemeinheit. Fachbereich Mathematik der Technischen Hochschule Darmstadt. Preprint-Nr. 1822, 1–19. Darmstadt, FB Mathematik
Wille R (1990) Concept Lattices and Conceptual Knowledge Systems. Report: TH Darmstadt. 1340, Darmstadt, TH Darmstadt, FB Mathematik
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2006). Introductory References. In: Brüggemann, R., Carlsen, L. (eds) Partial Order in Environmental Sciences and Chemistry. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-33970-1_18
Download citation
DOI: https://doi.org/10.1007/3-540-33970-1_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33968-7
Online ISBN: 978-3-540-33970-0
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)