164
L. Carlsen
Acknowledgments The author thanks dr. Rainer Bruggemann and dr. Jan W. Owsinski for
valuable comments.
References
Bruggemann, R., & Annoni, P. (2014). Average heights in partially ordered sets. MATCH –
Communications in Mathematical and in Computer Chemistry, 71, 117–142.
Bruggemann, R., & Carlsen, L. (Eds.). (2006a). Partial order in environmental sciences and
chemistry. Berlin: Springer.
Bruggemann, R., & Carlsen, L. (2006b). Introduction to partial order theory exemplified by
the evaluation of sampling sites. In R. Bruggemann & L. Carlsen (Eds.), Partial order in
environmental sciences and chemistry (pp. 61–110). Berlin: Springer.
Bruggemann, R., & Carlsen, L. (2011). An improved estimation of averaged ranks of partial orders.
MATCH – Communications in Mathematical and in Computer Chemistry, 65, 383–414.
Bruggemann, R., & Carlsen, L. (2012). Multicriteria 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, 425, 293–295.
Bruggemann, R., & Munzer, B. (1993). A graph-theoretical tool for priority setting of chemicals.
Chemosphere, 27, 1729–1736.
Bruggemann, R., & Patil, G. P. (2011). Ranking and prioritization for multi-indicator systems –
Introduction. New York: Springer.
Bruggemann, R., & Voigt, K. (1995). An evaluation of online databases by methods of lattice
theory. Chemosphere, 31, 3585–3594.
Bruggemann, R., & Voigt, K. (2008). Basic principles of Hasse diagram technique in chemistry.
Combinatorial Chemistry & High Throughput Screening, 11, 756–769.
Bruggemann, R., Carlsen, L., Voigt, K., & Wieland, R. (2014). PyHasse software for partial order
analysis: Scientific background and description of selected modules. In R. Bruggemann, L.
Carlsen, & J. Wittmann (Eds.), Multi-indicator systems and modelling in partial order (pp.
389–423). Springer: New York.
Bubley, R., & Dyer, M. (1999). Faster random generation of linear extensions. Discrete Mathematics, 201, 81–88.
De Loof, K., De Meyer, H., & De Baets, B. (2006). Exploiting the lattice of ideals representation
of a poset. Fundamenta Informaticae, 71, 309–321.
Ernesti, J., & Kaiser, P. (2008). Python – Das umfassende Handbuch. Bonn: Galileo Press.
Hetland, M. L. (2005). Beginning Python – From novice to professional. Berkeley: Apress.
Langtangen, H. P. (2008). Python scripting for computational science. Berlin: Springer.
NAS. (2014a). A framework to guide selection of chemical alternatives. The National Academies
Press at https://abm-website-assets.s3.amazonaws.com/laboratoryequipment.com/s3fs-public/
legacyimages/18872_0.pdf
NAS. (2014b). A framework to guide selection of chemical alternatives, report in brief, National
Academy of Science, Board on Chemical Sciences and Technology. http://dels.nas.edu/
resources/static-assets/materials-based-on-reports/reports-in-brief/Chemical-Alternatives.pdf
Python. (2015). Python. https://www.python.org/. Assessed Aug 2018.
Sørensen, P. B., Mogensen, B. B., Carlsen, L., & Thomsen, M. (2000). The influence of
partial order ranking from input parameter uncertainty. Definition of a robustness parameter.
Chemosphere, 41, 595–601.
TURI. (2006). Five chemicals alternatives assessment study, the Massachusetts toxics use reduction Institute, University of Massachusetts Lowell. https://www.turi.org/TURI_Publications/
TURI_Methods_Policy_Reports/Five_Chemicals_Alternatives_Assessment_Study._2006
Weigend, M. (2006). Objektorientierte Programmierung mit Python. Bonn: mitp-Verlag.
L. Carlsen
Acknowledgments The author thanks dr. Rainer Bruggemann and dr. Jan W. Owsinski for
valuable comments.
References
Bruggemann, R., & Annoni, P. (2014). Average heights in partially ordered sets. MATCH –
Communications in Mathematical and in Computer Chemistry, 71, 117–142.
Bruggemann, R., & Carlsen, L. (Eds.). (2006a). Partial order in environmental sciences and
chemistry. Berlin: Springer.
Bruggemann, R., & Carlsen, L. (2006b). Introduction to partial order theory exemplified by
the evaluation of sampling sites. In R. Bruggemann & L. Carlsen (Eds.), Partial order in
environmental sciences and chemistry (pp. 61–110). Berlin: Springer.
Bruggemann, R., & Carlsen, L. (2011). An improved estimation of averaged ranks of partial orders.
MATCH – Communications in Mathematical and in Computer Chemistry, 65, 383–414.
Bruggemann, R., & Carlsen, L. (2012). Multicriteria 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, 425, 293–295.
Bruggemann, R., & Munzer, B. (1993). A graph-theoretical tool for priority setting of chemicals.
Chemosphere, 27, 1729–1736.
Bruggemann, R., & Patil, G. P. (2011). Ranking and prioritization for multi-indicator systems –
Introduction. New York: Springer.
Bruggemann, R., & Voigt, K. (1995). An evaluation of online databases by methods of lattice
theory. Chemosphere, 31, 3585–3594.
Bruggemann, R., & Voigt, K. (2008). Basic principles of Hasse diagram technique in chemistry.
Combinatorial Chemistry & High Throughput Screening, 11, 756–769.
Bruggemann, R., Carlsen, L., Voigt, K., & Wieland, R. (2014). PyHasse software for partial order
analysis: Scientific background and description of selected modules. In R. Bruggemann, L.
Carlsen, & J. Wittmann (Eds.), Multi-indicator systems and modelling in partial order (pp.
389–423). Springer: New York.
Bubley, R., & Dyer, M. (1999). Faster random generation of linear extensions. Discrete Mathematics, 201, 81–88.
De Loof, K., De Meyer, H., & De Baets, B. (2006). Exploiting the lattice of ideals representation
of a poset. Fundamenta Informaticae, 71, 309–321.
Ernesti, J., & Kaiser, P. (2008). Python – Das umfassende Handbuch. Bonn: Galileo Press.
Hetland, M. L. (2005). Beginning Python – From novice to professional. Berkeley: Apress.
Langtangen, H. P. (2008). Python scripting for computational science. Berlin: Springer.
NAS. (2014a). A framework to guide selection of chemical alternatives. The National Academies
Press at https://abm-website-assets.s3.amazonaws.com/laboratoryequipment.com/s3fs-public/
legacyimages/18872_0.pdf
NAS. (2014b). A framework to guide selection of chemical alternatives, report in brief, National
Academy of Science, Board on Chemical Sciences and Technology. http://dels.nas.edu/
resources/static-assets/materials-based-on-reports/reports-in-brief/Chemical-Alternatives.pdf
Python. (2015). Python. https://www.python.org/. Assessed Aug 2018.
Sørensen, P. B., Mogensen, B. B., Carlsen, L., & Thomsen, M. (2000). The influence of
partial order ranking from input parameter uncertainty. Definition of a robustness parameter.
Chemosphere, 41, 595–601.
TURI. (2006). Five chemicals alternatives assessment study, the Massachusetts toxics use reduction Institute, University of Massachusetts Lowell. https://www.turi.org/TURI_Publications/
TURI_Methods_Policy_Reports/Five_Chemicals_Alternatives_Assessment_Study._2006
Weigend, M. (2006). Objektorientierte Programmierung mit Python. Bonn: mitp-Verlag.