Ranking of polluted regions in south west Germany based on a multi-indicator system

Match

Volumn 69, Issue 2, 2013, Pages 433-462

  Bruggemann, Rainer ^a   Mucha, Hans Joachim ^b   Bartel, Hans Georg ^c  

^a LEIBNIZ INSTITUTE OF FRESHWATER ECOLOGY AND INLAND FISHERIES   (Germany)

^b WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

^c HUMBOLDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84873849621     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (74)

1. Annoni, P. and K. Kozovska. 2010. EU Regional Competitiveness Index JRC 58169, EUR 24346 EN, 1-274. 2010. Luxembourg, Publications Office of the EU, EU. JRC Scientific and Technical Reports
2. Annoni, P. and R. Bruggemann. 2009. Exploring Partial Order of European Countries. Social Indicators Research 92:471-487.
3. Annoni, P., M. Fattore, and R. Bruggemann. 2008. Analyzing the Structure of Poverty by Fuzzy Partial Order. Pages 107-124 in J. Owsinski and R. Bruggemann, (eds.) Multicriteria Ordering and Ranking: Partial Orders, Ambiguities and Applied Issues. Systems Research Institute Polish Academy of Sciences, Warsaw.
4. Annoni.P., R. Bruggemann and.A. Saltelli. 2011. Partial order investigation of multiple indicator systems using variance based sensitivity analysis. Environ. Modelling and Software. 26: 950-958.
5. Bartel, H.-G., H.-J. Mucha, and J. Dolata 2003. Über eine Modifikation eines graphentheoretisch basierten partitionierenden Verfahrens der Clusteranalyse. Match-Commun.Math.Comput.Chem. 48: 209-223.
6. Brans, J. P. and P. H. Vincke. 1985. A Preference Ranking Organisation Method (The PROMETHEE Method for Multiple Criteria Decision-Making). Management Science 31:647-656.
7. Bruggemann, R. and G.P. Patil, 2010. Multicriteria Prioritization and Partial Order in environmental sciences. Environmental and Ecological Statistics 17(4), 383-410.
8. Bruggemann, R. and G.P. Patil, 2011. Ranking and Prioritization with Multi-Indicator Systems, Introduction to Partial Order and Its Applications. Springer, New York. 337 pp.
9. Bruggemann, R. and K. Voigt. 1995. An evaluation of online databases by methods of Lattice Theory. Chemosphere 31(7):3585-3594.
10. Bruggemann, R. and K. Voigt. 2006. Evaluation of the Pollution State in Baden-Wuerttemberg by a Local Analysis. Pages 121-135 in J. Studzinski and O. Hryniewicz, (eds.). Development of Methods and Technologies of Informatics for Process Modeling and Management. Polish Academy of Sciences, System Research Institute, Warsaw.
11. Bruggemann, R. and K. Voigt. 2008. Basic principles of Hasse Diagram technique in chemistry. Combinatorial Chemistry and High Throughput Screening 11:756-769.
12. Bruggemann, R. and K. Voigt. 2011. A New Tool to Analyze Partially Ordered Sets. Application: ranking of polychlorinated biphenyls and alkanes/alkenes in river Main, Germany. Match-Commun.Math.Comput.Chem. 66:231-251.
13. Bruggemann, R. and K. Voigt. 2012. Antichains in partial order, example: pollution in a German region by Lead, Cadmium, Zinc and Sulfur in the herb layer. Match-Commun.Math.Comput.Chem. 67:731-744.
14. Bruggemann, R. and L.Carlsen. 2011. An improved estimation of averaged ranks of partial orders. Match-Commun.Math.Comput.Chem 65(2), 383-414.
15. Bruggemann, R., A. Kerber, and G. Restrepo. 2011. Ranking Objects Using Fuzzy Orders, with an Application to Refrigerants. Match-Commun.Math.Comput. Chem. 66:581-603.
16. Bruggemann, R., E. Halfon, G. Welzl, K. Voigt, and C.E.W. Steinberg. 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.
17. Bruggemann, R., G. Welzl, and K. Voigt. 2003. Order theoretical tools for the evaluation of complex regional pollution patterns. J. Chem. Inf. Comp. Sc. 43:1771-1779.
18. Bruggemann, R., K. Voigt, A. Kaune, S. Pudenz, D. Komossa, and J. Friedrich. 1998. Vergleichende ökologische Bewertung von Regionen in Baden-Württemberg GSFBericht 20/98. GSF, Neuherberg.
19. Bruggemann, R., K. Voigt, G. Restrepo, and U. Simon. 2008. The concept of stability fields and hot spots in ranking of environmental chemicals. Environ Modelling and Software 23:1000-1012.
20. Bruggemann, R., P. B. Sørensen, D. Lerche, and L. Carlsen. 2004. Estimation of averaged ranks by a Local Partial Order model. J. Chem. Inf. Comp. Sc. 44:618-625.
21. Bruggemann, R., S. Pudenz, K. Voigt, A. Kaune, and K. Kreimes. 1999. An algebraic/graphical tool to compare ecosystems with respect to their pollution. IV: Comparative regional analysis by Boolean arithmetics. Chemosphere 38:2263-2279.
22. Bruggemann, R., U. Simon, and S. Mey. 2005. Estimation of averaged ranks by extended local partial order models. Match-Commun.Math.Comput.Chem. 54:489-518.
23. Bruggemann, R., L. Carlsen, 2012. Multi-criteria decision analyses. Viewing MCDA in terms of both process and aggregation methods: Some thoughts, motivated by the paper of Huang, Keisler and Linkov. Science of the Total Environment. doi: 10.1016/j.scitotenv.2012.02.062
24. Bubley, R. and M. Dyer. 1999. Faster random generation of linear extensions. Discr.Math. 201:81-88.
25. Carlsen, L. 2008. Hierarchical partial order ranking. Environmental Pollution 155:247-253.
26. Carlsen, L., D. B. Lerche, and P. B. Sørensen. 2002. Improving the predicting power of partial order based QSARs through linear extensions. J. Chem. Inf. Comp. Sc. 42:806-811.
27. Cherchye, L., E. Ooghe, and T. Van Puyenbroeck. 2010. Robust human development rankings. J. Econ. Inequal . DOI: 10.1007/s10888-007-1058-8
28. De Loof, K., B. De Baets, H. De Meyer, and R. Bruggemann. 2008. A hitchhiker's guide to poset ranking. Combinatorial Chemistry and High Throughput Screening 11:734-744.
29. De Loof, K., B.De Baets and H. De Meyer. 2011. Approximation of average ranks in posets. Match-Commun.Math.Comput.Chem.66(1):216-229.
30. De Loof, K., H. De Meyer, and B. De Baets. 2006. Exploiting the lattice of ideals representation of a Poset. Fundamenta Informaticae 71:309-321.
31. De Loof, K., M. Rademaker, R. Brüggemann, H. De Meyer, G. Restrepo, and B. De Baets. 2012. Order Theoretical Tools to Support Risk Assessment of Chemicals. Match-Commun.Math.Comput.Chem. 67:213-230.
32. Efron, B. 1979. Bootstrap methods: Another look at the jackknife. Annals of Statistics 7: 1-26.
33. Falbo, P., M. Fattore, and S. Stefani. 2010. A new index for electricity spot markets. Energy Policy 38:2739-2750.
34. Fattore, M. 2008. Hasse Diagrams, Poset Theory and Fuzzy Poverty Measures. Rivista Internazionale die Scienze Sociali 1:63-75.
35. Fattore, M. 2010. Axiomatic properties of geo-logarithmic price indices. J.of Econometrics 156: 344-353.
36. Hartigan, J. 1969. Using subsample values as typical values. Journal of the American Statistical Association 64: 1303-1317.
37. Hennig C. 2007. Cluster-wise assessment of cluster stability. Computational Statistics and Data Analysis 52: 258-271.
38. Huang, I. B., J. Keisler, and I. Linkov. 2011. Multi-criteria decision analysis in environmental sciences: Ten years of applications and trends. Science of the Total Environment 409:3578-3594.
39. Hubert, L.J., and P. Arabie 1985. Comparing partitions. Journal of Classification 2: 193-218.
40. Klein, D. J. and J. Brickmann. 2000. Partial Orderings in Chemistry. Comm.in math.and in comp.chemistry (match) 42: special issue.
41. Klein, D. J. and T. Ivanciuc. 2006. Directed Reaction Graphs as Posets. Pages 35-57 in R. Brüggemann and L. Carlsen, eds. Partial Order in Environmental Sciences and Chemistry. Springer-Verlag, Berlin.
42. Lerche, D., P. B. Sørensen, and R. Bruggemann. 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. 43:1471-1480.
43. Luther, B., R. Bruggemann, and S. Pudenz. 2000. An approach to combine cluster analysis with order theoretical tools in problems of environmental pollution. Match-Commun.Math.Comput.Chem. 42:119-143.
44. MacQueen, J. B. 1967. Some Methods for Classification and Analysis of Multivariate Observations. In: L. LeCam and J. Neyman (Eds.): Proc. 5th Berkeley Symp. Math. Statist. Prob., Vol. 1. Univ. California Press, Berkeley, 281-297
45. Mucha, H.-J. 1992. Clusteranalyse mit Mikrocomputern. Akademie Verlag, Berlin.
46. Mucha, H.-J. 2002. Clustering Techniques Accompanied by Matrix Reordering Techniques. In: K. Voigt and G. Welzl (Eds.): Order Theoretical Tools in Environmental Sciences. Shaker Verlag, Aachen, 129-140.
47. Mucha, H.-J. 2009. Cluscorr98 for Excel 2007: Clustering, Multivariate Visualization, and Validation. In: Mucha H.-J. and G. Ritter (Eds.), Classification and Clustering: Models, Software and Applications, Report No. 26 (http://www.wias-berlin.de/), WIAS, Berlin, 14-40.
48. Mucha, H.-J., H.-G. Bartel, and J. Dolata 2005. Techniques of rearrangements in binary trees (dendrograms) and applications. Match-Commun.Math.Comput.Chem.54: 561-582.
49. Mucha, H.-J., U. Simon, and R. Bruggemann. 2002. Model-based cluster analysis applied to flow cytometry data of phytoplankton. Technical Report No. 5 (http://www.wias-berlin.de/), WIAS, Berlin.
50. Munda, G. 2008. Social Multi-Criteria Evaluation for a Sustainable Economy. Springer-Verlag, Berlin.
51. Munda, G. and M. Nardo. 2008. Noncompensatory/nonlinear composite indicators for ranking countries: a defensible setting. Applied Economics 2008:1-11.
52. N.Nu, 2009. Progress towards the Lisbon Objectives in Education and Training-Indicators and Benchmarks, 2009. EU. Commission Staff Working Document, 1-181. 2009. JRC, Ispra, EU DG Education and Culture. Report of Commission of the European Communities.
53. Nardo, M. 2008. Handbook on Constructing Composite Indicators-Methodology and User Guide. OECD, Ispra.
54. Owsinski, J. W. 2011. The bi-partial approach in clustering and ordering: the model and the algorithms. Statistica and Applicazioni, special issue, 43-59.
55. Owsinski, J. W. 2012. Clustering and ordering via the bi-partial approach: the rationale, the model and some algorithmic considerations. In: J. Pociecha and R. Decker (Eds.): Data analysis methods and its applications. Wydawnictwo C. H. Beck, Warszawa, 109-124.
56. Rand, W.M. 1971. Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association 66: 846-850.
57. Randic, M. 1990. The nature of chemical structure. J.Math.Chem. 4:157-184.
58. Restrepo, G., E. J. Llanos, and H. Mesa. 2006. Topological space of the chemical elements and its properties. J.Math.Chem. 39:401-416.
59. Restrepo, G., H. Mesa, and E. J. Llanos. 2007. Three Dissimilarity Measures to Contrast Dendrograms. J. Chem. Inf. Model. 47:761-770.
60. Restrepo, G., H. Mesa, and J. L. Villaveces. 2005. On the topological sense of chemical sets. J. Math. Chem. 39:363-376.
61. Restrepo, G. and D. J. Klein. 2011. Predicting densities of nitrocubanes using partial orders. J. Math. Chem. 49:1311-1321.
62. Restrepo, G., H. Mesa, 2011. Chemotopology. Current Computer-Aided Drug design 7:90-97.
63. Roy, B. 1990. The outranking approach and the foundations of the ELECTRE methods. Pages 155-183 in Bana e Costa, ed. Readings in Multiple Criteria Decision Aid. Springer-Verlag, Berlin.
64. Ruch, E. 1975. The diagram lattice as Structural Principle. Theor.Chim.Acta 38:167-183.
65. Ruch, E. and I. Gutman. 1979. The Branching Extent of Graphs. J.of Combinatorics-Inform.System Sciences 4:285-295.
66. Schneeweiss, C. 1991. Planung 1-Systemanalytische und entscheidungstheoretische Grundlagen. Springer-Verlag, Berlin.
67. Simon, U., R. Bruggemann, S. Mey, and S. Pudenz. 2005. METEOR-application of a decision support tool based on discrete mathematics. Match-Commun.Math. Comput.Chem. 54:623-642
68. Sørensen, P. B. and D. Lerche. 2002. Quantification of the Uncertainty Related to the Use of a Limited Number of Random Linear Extensions. Pages 65-72 in K. Voigt and G. Welzl, eds. Order Theoretical Tools in Environmental Sciences-Order Theory (Hasse diagram technique) Meets Multivariate Statistics. Shaker, Aachen.
69. Sørensen, P. B., R. Bruggemann, L. Carlsen, B. B. Mogensen, J. Kreuger, and S. Pudenz. 2003. Analysis of monitoring data of pesticide residues in surface waters using partial order ranking theory. Envir.Tox.Chem. 22:661-670.
70. Steinhaus, H. 1956. Sur la division des corps matériels en parties. Bulletin de l'Academie Polonaise de Sciences, Vol. IV, 12, 801-804.
71. Tsakovski, S. and V. Simeonov. 2008. Hasse Diagrams as Explanatory Tool in Environmental Data Mining: A Case Study. Pages 50-68 in J. Owsinski and R. Bruggemann, eds. Multicriteria Ordering and Ranking: Partial Orders, Ambiguities and Applied Issues. Systems Research Institute Polish Academy of Sciences, Warsaw.
72. Voigt, K., H. Scherb, R. Bruggemann, and K.-W. Schramm. 2011. Application of the PyHasse Program Features: Sensitivity, Similarity, and Separability for Environmental Health Data. Statistica & Applicazioni, Special Issue,:155-168.
73. Winkler, P. 1982. Average height in a partially ordered set. Discr.Math. 39:337-341.
74. Yager, R. R. 1988. On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transactions on Systems, Man and Cybernetics 18:183-190.