Partial Order in Environmental Chemistry

Author(s): Rainer Bruggemann*, Lars Carlsen

Journal Name: Current Computer-Aided Drug Design

Volume 16 , Issue 3 , 2020


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Graphical Abstract:


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.

[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.


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VOLUME: 16
ISSUE: 3
Year: 2020
Published on: 02 June, 2020
Page: [257 - 269]
Pages: 13
DOI: 10.2174/1573409915666190416160350
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