https://doi.org/10.4081/peasa.13
On a mathematical theory of sustainability assessment
Published: November 4, 2022
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All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.
We compile a number of postulates to be satisfied by a function that mathematically assesses sustainability of some type: national, urban, energy, etc. These postulates lay the mathematical foundations of a sustainability theory and lead to a simple model based on shifted geometric means combining basic sustainability indicators into an overall index. The model has a number of desirable properties and generalizes the weighted arithmetic and weighted geometric means, which are commonly used aggregation functions in sustainability assessments. Numerical results demonstrate the closeness of the model to other established techniques of sustainability.
Beliakov, G., Pradera, A., and Calvo, T. (2007). Aggregation Functions: A Guide for Practitioners. Berlin, Springer-Verlag.
Esty, D. C., Levy, M., Srebotnjak, T., and de Sherbinin, A. (2005). Environmental Sustainability Index: Benchmarking National Environmental Stewardship. New Haven, CT, Yale Center for Environmental Law and Policy. http://sedac.ciesin.columbia.edu/es/esi/ESI2005.pdf
Gan, X., Fernandez, I. C., Guo, J., Wilson, M., Zhao, Y., Zhou, B., and Wu, J. (2017). When to use what: Methods for weighting and aggregating sustainability indicators. Ecol Indic 81:491-502.
DOI: https://doi.org/10.1016/j.ecolind.2017.05.068
Greco, S., Ishizaka, A., Tasiou, M., and Torrisi, G. (2019). On the methodological framework of composite indices: A review of the issues of weighting, aggregation, and robustness. Social Indic Res 141:61-94.
DOI: https://doi.org/10.1007/s11205-017-1832-9
Grigoroudis, E., Kouikoglou, V. S., and Phillis, Y. A. (2021). SAFE 2019: Updates and new sustainability findings worldwide. Ecol Indic 121:107072.
DOI: https://doi.org/10.1016/j.ecolind.2020.107072
Hardy, G. H., Littlewood, J. E., and Polya, G. (1934). Inequalities. London, Cambridge University Press.
Hwang, C. L., and Yoon, K. (1981). Multiple Attribute Decision Making. Berlin, Springer.
DOI: https://doi.org/10.1007/978-3-642-48318-9
van de Kerk, G., and Manuel, A. R. (2008). A comprehensive index for a sustainable society: The SSI—the Sustainable Society Index. Ecol Econom 66:228-242.
DOI: https://doi.org/10.1016/j.ecolecon.2008.01.029
Kolmogorov, A. (1930). Sur la notion de la moyenne. Atti dell'Accademia Nazionale dei Lincei 12:388-391. Also in: Kolmogorov, A. (1991). Selected Works I: Mathematics and Mechanics. Dordrecht, Kluwer Academic Publishers, pp. 144-146.
Liu, K. F. (2007). Evaluating environmental sustainability: an integration of multiple-criteria decision-making and fuzzy logic. Environ Manage 39,:721-736.
DOI: https://doi.org/10.1007/s00267-005-0395-8
Nagumo, M. (1930). Über eine klasse der mittelwerte. Japanese Journal of Mathematics: Transactions and Abstracts 7:71-79.
DOI: https://doi.org/10.4099/jjm1924.7.0_71
OECD (1991). Environmental Indicators: A Preliminary Set. Paris, OECD.
Rockström, J., Steffen, W., Noone, K., Persson, Å., Chapin III, F. S., Lambin, E., et al. (2009). Planetary boundaries: exploring the safe operating space for humanity. Ecol Soc 14: 26268316.
Saaty, T.L., 1980. The Analytic Hierarchy Process. New York, McGraw Hill.
DOI: https://doi.org/10.21236/ADA214804
United Nations Development Programme (2022). Human Development Index (HDI). https://hdr.undp.org/data-center/human-development-index#/indicies/HDI
Wolf, M. J., Emerson, J. W., Esty, D. C., de Sherbinin, A., Wendling, Z. A., et al. (2022). 2022 Environmental Performance Index. New Haven, CT, Yale Center for Environmental Law and Policy. https://epi.yale.edu
Yang, L., (2014). An Inventory of Composite Measures of Human Progress. Technical report, United Nations Development Programme Human Development Report Office. https://hdr.undp.org/content/inventory-composite-measures-human-progress
How to Cite
Phillis, Y. A., Kouikoglou, V. S., Grigoroudis, E., & Kanellos, F. D. (2022). On a mathematical theory of sustainability assessment. Proceedings of the European Academy of Sciences and Arts, 1(1). https://doi.org/10.4081/peasa.13
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