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My interest in the theory of ranking and its application to the assessment of the environmental hazard of toxic contaminants evolved from a collaboration that I started with the Italian scientist Marcello Reggiani in 1979. It occurred to me that we could use graphs and Hasse diagrams to display the hazard of toxic contaminants to the environment. The advantage of using Hasse diagrams is that we can also display the contradictions in the data that are used to create the ranking. Several biological and physical-chemical properties, such as contaminant toxicity or their accumulation in fish, are used for ranking. Dr. Reggiani and I developed the software we called HASSE. Later a German scientist, Dr. Rainer Brüggemann, became also interested in this topic we have collaborated since 1989. He has expanded on the theoretical foundations of the method, expanded the software with more options (The program can be obtained from Dr. Brüggemann). Since 1998 he has organized an annual international workshop on the use of Hasse diagrams that takes place in Europe every winter.

Halfon, E. and Reggiani, M.G., 1986. On ranking chemicals for environmental hazard. Environ. Science Tech., 20: 1173-1179.

Reggiani, M.G. and Halfon, E. 1988. An improved ranking scheme for environmental hazard. In A. Marani (Ed.) Advances in Environmental Modelling, Elsevier, Amsterdam, pp. 183-194.

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. 1989. The application of ecological modelling to toxic contaminants and ecosystem stress. Water Poll. Res. J. Canada, 24:323-343.

Halfon, E. and R. Brüggemann. 1989. Environmental hazard ranking of chemicals spilled in the Rhine River in November 1986. Acta hydrochim. hydrobiol., 17: 47-60.

Halfon, E. and R. Brüggemann. 1989. Environmental hazard of eight chemicals in the Rhine River. Wat. Sci. Tech., 21: 815-820.

Brüggemann, R. and Halfon, E. 1989. A ranking analysis of contaminated sites along the shores of lake Ontario. NWRI Report No. 89-22.

Brüggemann, R. and Halfon, E. 1990. Ranking for environmental hazard of the chemicals spilled in the Sandoz accident in November 1986. Sci. Tot. Environ. 97:827-837

Halfon, E. and Brüggemann, R. 1990. Simulation of disulfoton fate in the River Rhine with the TOXFATE model, Sci. Tot. Environ., 97: 385-394.

Halfon, E., B. Altschuh and Brüggemann, R. 1991. Estimations of aqueous solubility for octanol/water partition coefficient analyzed by the bootstrap method. Chemosphere, 22:953-957.

Brüggemann, R. and Halfon E. 1991. Analysis of Hasse diagrams. NWRI Report.

Brüggemann, R. and Halfon, E. 1994. Sensitivity analysis of partially ordered sets and ranking objects of environmental interest. NWRI Contribution No. 94-95.

Brüggemann, R. Munzer, B. and 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.

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

Brüggemann, R. and Halfon, E. 1995. Theoretical base of the program "Hasse". GSF, Technical report, Bericht 20/95. 67 pp.

Brüggemann, R., Voigt, K and Halfon, E. 1996. Partially ordered sets - A computerized tool to compare environmental databases. In Environmental Software Systems, R. Denzer, G. Schimak and D. Russell (Eds.) Proceedings of the International Symposium on Environmental Software Systems, 1995, Chapman & Hall, pp. 185-195.

Halfon, E., Galassi, S., Brüggemann, R., and Provini, A. 1996. Selection of priority properties to assess environmental hazard of pesticides. Chemosphere 33:1543-1562

Galassi, S., A. Provini, E. Halfon, 1996. Risk Assessment for Pesticides and Their Metabolites in Water. Intern J Environ Anal Chem, 65, 331-344.

Brüggemann, R. and Halfon, E. 1997. Comparative Analysis of Nearshore Contaminated Sites in Lake Ontario: Ranking for Environmental Hazard, J. Environ. Sci. Health, 32: 277-292

Halfon, E. and Brüggemann, R. 1998. On ranking chemicals for environmental hazard. Comparison of methodologies. Proceedings of the workshop on Order Theoretical Tools in Environmental Sciences, Berlin, pp. 11-48.

Brüggemann,R., Halfon,E., 2000. Introduction into the basic principles of ranking theory by partial order. Proceedings of the Second workshop on the use of Hasse diagrams, Roskilde, Denmark, October 1999.

Brüggemann, R., Halfon, E., Pudenz, R., Simon, G. and Luther, M. 2000. New tools for the analysis of Hasse diagrams for ranking chemicals. Proceedings of the Second workshop on the use of Hasse diagrams, Roskilde, Denmark, October 1999.

Halfon,E., Brüggemann, 2001. Evaluation of test battery results for the toxicity of chemicals in sediments of Lake Ontario. J. Chemical Information and Computer Science. 41: 918-925.

Halfon, E., 2006. Hasse diagrams and software development. In R. Brüggemann and L. Carlsen, Eds. Partial Order in Environmental Sciences and Chemistry,Springer, 385-392.