Partial Order in Environmental Chemistry

Rainer       Bruggemann; Lars       Carlsen

Abstract

Background: The theory of partial order is a branch of Discrete Mathematics and is often seen as pretty esoteric. However, depending on a suitable definition of an order relation, partial order theory has some statistical flavor. Here we introduce the application of partial order for environmental chemistry.

Objective: We showed that partial order is an instrument, which at the same time, has both data exploration - and evaluation potency.

Methods: The partial order theory was applied in this study. It depends on four indicators which describe the environmental hazards of chemicals.

Results: Nineteen organic chemicals were found within a monitoring study in the German river Main and were taken as an exemplary case. The results indicated that chemicals can have a high risk on the environment, however, the type of risk is different and should not conceptually merge into a single quantity.

Conclusion: Partial order theory is of help to define different regulations and environmental management plans.

Keywords: Partial order, decision making, environmental chemicals, descriptors of chemicals behavior, indicators, processoriented mathematical models, antichain matrix, graph-theoretical structure.

« Previous Next »

Graphical Abstract

[1] 
Wiberg, E. Die chemische Affinität. Eine erste Einführung in die Lehre von der Triebkraft chemischer Reaktionen; Walter de Gruyter: Berlin, 1972. 
[http://dx.doi.org/10.1515/9783110826074] 
[2] 
Hollemann, A.F.; Wiberg, E. Lehrbuch der Anorganischen Chemie; Walter de Gruyter: Berlin, 2007. 
[http://dx.doi.org/10.1515/9783110177701] 
[3] 
Schneider, W. Einführung in die Koordinationschemie; Springer-Verlag: Berlin, 1968. 
[http://dx.doi.org/10.1007/978-3-642-92969-4] 
[4] 
Hudson, R.F.  Displacement Reactions and the Concept of Soft and
Hard Acids and Bases. Structure and Bonding; Jörgensen, C.K.;
Neilands, J.B.; Nyholm, R.S.; Reinen, D.; Williams, R.J.P., Eds.;
Springer-Verlag: Berlin, 1966, Vol. 1, pp. 221-233.
[http://dx.doi.org/10.1007/BFb0119553] 
[5] 
Atkins, P.W. Quanta - A Handbook of Concepts; Oxford University Press: Oxford, 1991. 
[6] 
Ivanciuc, T.; Ivanciuc, O.; Klein, D.J. Posetic quantitative superstructure/activity relationships (QSSARs) for chlorobenzenes. J. Chem. Inf. Model.,  2005, 45(4), 870-879.
[http://dx.doi.org/10.1021/ci0501342] [PMID: 16045280] 
[7] 
Klein, D. J. Mathematical Chemistry! Is it? And if so. What is it? Hyle-Int.Journ. Philosophy of Chemistry,  2014, 19, 55-85.
[8] 
Restrepo, G.; Mesa, H.; Llanos, E.J.; Villaveces, J.L. Topological study of the periodic system. J. Chem. Inf. Comput. Sci.,  2004, 44(1), 68-75.
[http://dx.doi.org/10.1021/ci034217z] [PMID: 14741012] 
[9] 
Hefferlin, R. The Periodic Systems of Molecules - Presuppositions, Problems, and Prospects.Philosophy of Chemistry; Baird, D., Ed.; Springer, Netherlands, 2006, pp. 221-243.
[http://dx.doi.org/10.1007/1-4020-3261-7_12] 
[10] 
Restrepo, G.; Llanos, E.J.; Mesa, H. Topological space of the chemical elements and its properties. J. Math. Chem.,  2006, 39, 401-416.
[http://dx.doi.org/10.1007/s10910-005-9041-1] 
[11] 
Kerber, A.; Laue, R.; Moser, D. Ein Strukturgenerator für molekulare Graphen. Anal. Chim. Acta,  1990, 235, 221-228.
[http://dx.doi.org/10.1016/S0003-2670(00)82078-4] 
[12] 
Braun, J.; Gugisch, R.; Kerber, A.; Laue, R.; Meringer, M.; Rücker, C. MOLGEN-CID--A canonizer for molecules and graphs accessible through the Internet. J. Chem. Inf. Comput. Sci.,  2004, 44(2), 542-548.
[http://dx.doi.org/10.1021/ci030404l] [PMID: 15032534] 
[13] 
Restrepo, G.; Stadler, P.F. Assessing Greenness of Chemical Reactions and Synthesis Plans through Posetic Landscapes. ACS Sustain. Chem.& Eng.,  2016, 4, 2191-2199.
[http://dx.doi.org/10.1021/acssuschemeng.5b01649] 
[14] 
Mathematics in Chemistry Meeting.  Lipsia, Restrepo, G., Ed.;
  2016. MATCH Commun.Math.Comput.Chem , 2018; 80, . (3)
[15] 
Mackay, D.; Joy, M.; Paterson, S. A Quantitative Water, Air, Sediment Interaction (QWASI) Fugacity Model for Describing the Fate of Chemicals in Lakes. Chemosphere,  1983, 12, 981-997.
[http://dx.doi.org/10.1016/0045-6535(83)90251-5] 
[16] 
Mackay, D.; Paterson, S.; Joy, M. A Quantitative Water, Air, Sediment Interaction (QWASI) Fugacity Model for Describing the Fate of Chemicals in Rivers. Chemosphere,  1983, 12, 1193-1208.
[http://dx.doi.org/10.1016/0045-6535(83)90125-X] 
[17] 
Brüggemann, R.; Restrepo, G.; Voigt, K. Structure-fate relationships of organic chemicals derived from the software packages E4CHEM and WHASSE. J. Chem. Inf. Model.,  2006, 46(2), 894-902.
[http://dx.doi.org/10.1021/ci050424i] [PMID: 16563021] 
[18] 
Matthies, M.; Bruggemann, R.; Münzer, B.; Schernewski, G.; Trapp, S. Exposure and Ecotoxicity Estimation for Environmental Chemicals (E4CHEM): Application of Fate Models for Surface Waters and Soils. Ecol. Modell.,  1989, 47, 115-130.
[http://dx.doi.org/10.1016/0304-3800(89)90112-9] 
[19] 
Bruggemann, R.; Drescher-Kaden, U. Einführung in die modellgestützte Bewertung von Umweltchemikalien - Datenabschätzung, Ausbreitung, Verhalten, Wirkung und Bewertung; Springer-Verlag: Berlin, 2003. 
[http://dx.doi.org/10.1007/978-3-642-55695-1] 
[20] 
Berding, V.; Matthies, M. European scenarios for EUSES regional distribution model. Environ. Sci. Pollut. Res. Int.,  2002, 9(3), 193-198.
[http://dx.doi.org/10.1007/BF02987488] [PMID: 12094533] 
[21] 
Verdonck, F.A.M.; Boeije, G.; Vandenberghe, V.; Comber, M.; de Wolf, W.; Feijtel, T.; Holt, M.; Koch, V.; Lecloux, A.; Siebel-Sauer, A.; Vanrolleghem, P.A. A rule-based screening environmental risk assessment tool derived from EUSES. Chemosphere,  2005, 58(9), 1169-1176.
[http://dx.doi.org/10.1016/j.chemosphere.2004.09.060] [PMID: 15667838] 
[22] 
Trapp, S.; Matthies, M. Chemodynamics and Environmental Modeling. An introduction; Springer-Verlag: Berlin, 1998. 
[http://dx.doi.org/10.1007/978-3-642-80429-8] 
[23] 
Brans, J.P.; Vincke, P.H. A Preference Ranking Organisation Method (The PROMETHEE Method for Multiple Criteria Decision - Making). Manage. Sci.,  1985, 31, 647-656.
[http://dx.doi.org/10.1287/mnsc.31.6.647] 
[24] 
Brans, J.P.; Vincke, P.H.; Mareschal, B. How to select and how to rank projects: The PROMETHEE method. Eur. J. Oper. Res.,  1986, 24, 228-238.
[http://dx.doi.org/10.1016/0377-2217(86)90044-5] 
[25] 
Roy, B. The outranking approach and the foundations of the ELECTRE methods  Readings in Multiple Criteria Decision Aid. ;
  in Bana, e Costa,., Ed.; Springer-Verlag, Berlin, , 1990,; pp. 155-183.
[http://dx.doi.org/10.1007/978-3-642-75935-2_8] 
[26] 
Roy, B.; Vanderpooten, D. The European School of MCDA: Emergence, Basic Features and Current Works. J.Multi-Crit. Decis. Anal.,  1996, 5, 22-38.
[27] 
Saaty, T.L. How to Make a Decision: The Analytical Hierarchy Process. Interfaces,  1994, 24, 19-43.
[http://dx.doi.org/10.1287/inte.24.6.19] 
[28] 
Munda, G. Social Multi-Criteria Evaluation for a Sustainable Economy; Springer-Verlag: Berlin, 2008. 
[http://dx.doi.org/10.1007/978-3-540-73703-2] 
[29] 
Figueira, J.; Greco, S.; Ehrgott, M. Multiple Criteria Decision Analysis, State of the Art Surveys; Springer: Boston, 2005. 
[http://dx.doi.org/10.1007/b100605] 
[30] 
Cronin, M.T.; Livingstone, D.J., Eds.; Predicting chemical toxicity and fate; CRC press, 2004. 
[31] 
Sahoo, S.; Adhikari, C.; Kuanar, M.; Mishra, B.K. A Short Review of the Generation of Molecular Descriptors and Their Applications in Quantitative Structure Property/Activity Relationships. Curr Comput Aided Drug Des,  2016, 12(3), 181-205.
[http://dx.doi.org/10.2174/1573409912666160525112114] [PMID: 27222031] 
[32] 
Basak, S.C.; Mishra, R.K. Editorial: Descriptor Spaces for QSAR: Delving into the History of the Expanding Frontier. Curr Comput Aided Drug Des,  2017, 13(1), 4-7.
[http://dx.doi.org/10.2174/157340991301170127200832] [PMID: 28222673] 
[33] 
Kier, L.B. Modeling Bacterial Infection Phenomena. Curr Comput Aided Drug Des,  2015, 11(4), 321-324.
[http://dx.doi.org/10.2174/1573409912666151218155921] [PMID: 26679632] 
[34] 
Basak, S.C. Mathematical descriptors for the prediction of property, bioactivity, and toxicity of chemicals from their structure: a chemical-cum-biochemical approach. Curr Comput Aided Drug Des,  2013, 9(4), 449-462.
[http://dx.doi.org/10.2174/15734099113096660041] [PMID: 24138422] 
[35] 
Mezey, P.G. Shape in Chemistry An Introduction to Molecular Shape and Topology; Verlag Chemie: Weinheim, 1993. 
[36] 
Mezey, P.G.; Zimpel, Z.; Warburton, P.; Walker, P.D.; Irvine, D.G.; Huang, X-D.; Dixon, D.G.; Greenberg, B.M. Use of Quantitative Shape-Activity Relationships to Model the Photoinduced Toxicity of Polycyclic Aromatic Hydrocarbons: Electron Densitiy Shape Features Accurately Predict Toxicity. Environ. Toxicol. Chem.,  1998, 17, 1207-1215.
[37] 
Klein, D.J.; Babic, D. Partial orderings in Chemistry. J. Chem. Inf. Comput. Sci.,  1997, 37, 656-671.
[http://dx.doi.org/10.1021/ci9601776] 
[38] 
Brüggemann, R.; Voigt, K. Basic principles of Hasse diagram technique in chemistry. Comb. Chem. High Throughput Screen.,  2008, 11(9), 756-769.
[http://dx.doi.org/10.2174/138620708786306005] [PMID: 18991578] 
[39] 
Halfon, E. Is there a best model structure? I: Modelling the fate of a toxic substance in a lake. Ecol. Modell.,  1983, 20, 135-152.
[http://dx.doi.org/10.1016/0304-3800(83)90003-0] 
[40] 
Halfon, E. Is there a best model structure? II. Comparing the Model Structures of Different Fate Models. Ecol. Modell.,  1983, 20, 153-163.
[http://dx.doi.org/10.1016/0304-3800(83)90004-2] 
[41] 
Halfon, E. Hasse Diagrams and Software Development.Partial Order in Environmental Sciences and Chemistry; Brüggemann, R; Carlsen, L., Ed.; Springer-Verlag: Berlin, 2006, pp. 385-392.
[http://dx.doi.org/10.1007/3-540-33970-1_17] 
[42] 
Halfon, E.; Reggiani, M.G. On Ranking Chemicals for Environmental Hazard. Environ. Sci. Technol.,  1986, 20, 1173-1179.
[http://dx.doi.org/10.1021/es00153a014] 
[43] 
Brüggemann, R.; Pudenz, S.; Voigt, K. Kaune, and Kreimes. K. An algebraic/graphical tool to compare ecosystems with respect to their pollution. IV: Comparative regional analysis by Boolean arithmetics. Chemosphere,  1999, 38, 2263-2279.
[http://dx.doi.org/10.1016/S0045-6535(98)00445-7] 
[44] 
Brüggemann, R.; Bartel, H-G. A Theoretical Concept to Rank Environmentally Significant Chemicals. J. Chem. Inf. Comput. Sci.,  1999, 39, 211-217.
[http://dx.doi.org/10.1021/ci9800559] 
[45] 
Brüggemann, R.; Patil, G.P. Ranking and Prioritization for Multi-indicator Systems - Introduction to Partial Order Applications; Springer: New York, 2011. 
[46] 
Hasse, H. Vorlesungen über Klassenkörpertheorie; Physica-Verlag: Marburg, 1967. 
[47] 
Van de Walle, B.; De Baets, B.; Kersebaum, K.C. Fuzzy multi-criteria analysis of cutting techniques in a nuclear dismantling project. Fuzzy Sets Syst.,  1995, 74, 115-126.
[http://dx.doi.org/10.1016/0165-0114(95)00017-F] 
[48] 
Van de Walle, B.; De Baets, B.; Kerre, E. Characterizable fuzzy preference structures. Ann. Oper. Res.,  1998, 80, 105-136.
[49] 
Bruggemann, R.; Carlsen, L. An attempt to Understand Noisy Posets. MATCH Commun.Math.Comput.Chem.,  2016, 75, 485-510.
[50] 
Bruggemann, R.; Kerber, A.; Restrepo, G. Ranking Objects Using Fuzzy Orders, with an Application to Refrigerants. MATCH Commun.Math.Comput.Chem.,  2011, 66, 581-603.
[51] 
Wieland, R.; Bruggemann, R. Hasse Diagram Technique and Monte Carlo Simulations, MATCH Commun. Math.Comput.Chem.,  2013, 70, 45-49.
[52] 
Bruggemann, R.; Kerber, A. Fuzzy Logic and Partial Order; First Attempts with the new PyHasse-Program L_eval. MATCH Commun.Math.Comput.Chem.,  2018, 80, 745-768.
[53] 
Bruggemann, R.; Carlsen, L. Incomparable-What now? MATCH Commun.Math.Comput.Chem.,  2014, 71, 699-714.
[54] 
Bruggemann, R.; Carlsen, L. Incomparable: what now II? Absorption of incomparabilities by a cluster method. Qual. Quant.,  2014, 49, 1633-1645.
[http://dx.doi.org/10.1007/s11135-014-0076-x] 
[55] 
Bruggemann, R.; Carlsen, L. Incomparable - What Now III. Incomparabilities, Elucidated by a Simple Version of ELECTRE III and a Fuzzy Partial Order Approach. MATCH Commun.Math.Comput.Chem.,  2015, 73, 277-302.
[56] 
Bruggemann, R.; Carlsen, L. Incomparable: What now, IV. Incomparabilities: A Modelling challenge.Partial Order Concepts in Applied Sciences; Fattore, M; Brüggemann, R., Ed.; Springer: Cham, Switzerland, 2017, pp. 35-47.
[http://dx.doi.org/10.1007/978-3-319-45421-4_3] 
[57] 
Bruggemann, R.; Voigt, K. 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.,  2012, 67, 731-744.
[58] 
Arcagni, A. PARSEC:An R Package for Partial Orders in Socio-Economics.Partial Order Concepts in Applied Sciences; Fattore. M; Brüggemann, R., Ed.; Springer: Cham, 2017, pp. 275-289.
[http://dx.doi.org/10.1007/978-3-319-45421-4_19] 
[59] 
R Core Team R. a language and environment for statistical computing,
 R Foundation for Statistical Computing. Vienna.  http://www.R-project.org/ (assessed January, the 3rd 2019
[60] 
Strangman, G.  Python libraries stats, pstat, A possible newer access
 by: https://warwick.ac.uk/fac/sci/moac/people/students/peter_cock/python/lin_reg/ 2008 (accessed 30.06.18)
[61] 
Bruggemann, R.; Carlsen, L.; Voigt, K.; Wieland, R. PyHasse Software for Partial Order Analysis: Scientific Background and Description of Selected Modules.Multi-indicator Systems and Modelling in Partial Order; Brüggemann, R.; Carlsen, L; Wittmann, J., Ed.; Springer: New York, 2014, pp. 389-423.
[http://dx.doi.org/10.1007/978-1-4614-8223-9_19] 
[62] 
Annoni, P.; Fattore, M.; Bruggemann, R.  2011 A Multi-Criteria
 Fuzzy Approach for Analyzing Poverty structure. Statistica & Applicazioni,
 special issue, 2011, 7-30. 
[63] 
Annoni, P.; Bruggemann, R.; Carlsen, L. Pecularities in Multidimensional Regional Poverty.Partial Order Concepts in Applied Sciences; Fattore, M; Bruggemann, R., Ed.; Springer: Cham, Switzerland, 2017, pp. 121-133.
[http://dx.doi.org/10.1007/978-3-319-45421-4_8] 
[64] 
Carlsen, L.; Bruggemann, R. An Analysis of the “Failed States Index” by Partial Order Methodology. J.of Soc. Struct (JOSS),  2014, 14, 1-31.
[65] 
Carlsen, L.; Bruggemann, R. The “Failed State Index” Offers More than Just a Simple Ranking. Soc. Indic. Res.,  2014, 115, 525-530.
[http://dx.doi.org/10.1007/s11205-012-9999-6] 
[66] 
Carlsen, L.; Bruggemann, R. Fragile State Index: Trends and Developments, A Partial Order Data Analysis. Soc. Indic. Res.,  2017, 133, 1-14.
[http://dx.doi.org/10.1007/s11205-016-1353-y] 
[67] 
Carlsen, L. Happiness as a sustainability factor. The world happiness index: a posetic - based data analysis. Sustain. Sci.,  2018, 13, 549-571.
[http://dx.doi.org/10.1007/s11625-017-0482-9] 
[68] 
Fattore, M. Functionals and Synthetic Indicators Over Finite Posets.Partial Order Concepts in Applied Sciences; Fattore, M; Brüggemann, R., Ed.; Springer: Cham, Switzerland, 2017, pp. 71-86.
[http://dx.doi.org/10.1007/978-3-319-45421-4_5] 
[69] 
Fattore, M.; Maggino, F.; Greselin, F.  2011 a. Socio-economic
 evaluation with ordinal variables: in-tegrating and poset approaches.
 Statistica & Applicazioni, 2011, special issue, 31-42. 
[70] 
Fattore, M.; Bruggemann, R.; Owsinski, J. Using Poset Theory to Compare Fuzzy Multidimensional Material Deprivation Across Regions.New Perspectives in Statistical Modeling and Data Analysis, Ingrassia, S; Rocci, R; Vichi, M., Ed.; Springer-Verlag: Heidelberg, 2011, pp. 49-56.
[http://dx.doi.org/10.1007/978-3-642-11363-5_6] 
[71] 
Fattore, M.; Maggino, F. 2014. Partial Orders in Socio-economics. A practical challenge for poset theorists or a cultural challenge for social scientists?Multi-indicator Systems and Modelling in Partial Order; Brüggemann, R.; Carlsen, L; Wittmann, J., Ed.; Springer: New York, 2014, pp. 197-214.
[http://dx.doi.org/10.1007/978-1-4614-8223-9_9] 
[72] 
Carlsen, L.; Sørensen, P.B.; Thomsen, M.; Brüggemann, R. QSAR’s based on partial order ranking. SAR QSAR Environ. Res.,  2002, 13(1), 153-165.
[http://dx.doi.org/10.1080/10629360290002307] [PMID: 12074384] 
[73] 
Mucha, H-J. Clustering Techniques accompanied by Matrix Reordering Techniques.Order Theoretical Tools in Environmental Sciences - Order Theory (Hasse diagram technique) Meets Multivariate Statistics; Voigt, K; Welzl, G., Ed.; Shaker-Verlag: Aachen, 2002, pp. 129-140.
[74] 
Bruggemann, R.; Voigt, K.; Restrepo, G.; Simon, U. The concept of stability fields and hot spots in ranking of environmental chemicals. Environ. Model. Softw.,  2008, 23, 1000-1012.
[http://dx.doi.org/10.1016/j.envsoft.2007.11.001] 
[75] 
Bruggemann, R.; Restrepo, G.; Voigt, K.; Annoni, P. Weighting Intervals and Ranking. Exemplified by Leaching Potential of Pesticides. MATCH Commun.Math.Comput.Chem.,  2013, 69, 413-432.
[76] 
Bruggemann, R.; Carlsen, L. Partial Order and Inclusion of Stakeholder’s Knowledge. MATCH Commun.Math.Comput.Chem.,  2018, 80, 769-791.
[77] 
Bruggemann, R. Indikatoren, partielle Ordnungen und Entscheidungsträger.Simulation in Umwelt- und Geowissenschaften, Wittmann, J; Berlin, W., Ed.; Shaker: Aachen, Berlin, 2017, pp. 9-18.

Rights & Permissions Print Cite

Article Metrics

22

1

Journal Information

For Authors

For Editors

For Reviewers

Explore Articles

Open Access

Open Access Articles

For Visitors

DOI https://dx.doi.org/10.2174/1573409915666190416160350	Print ISSN 1573-4099
Publisher Name Bentham Science Publisher	Online ISSN 1875-6697

Current Computer-Aided Drug Design

Partial Order in Environmental Chemistry

Abstract

Graphical Abstract

Related Journals

Related Books