Non-aggregated indicators of environmental sustainability
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In this paper, we propose a new way to assess and compare the sustainability level of countries, using concepts and tools from the theory of partially ordered sets. Using so-called average height and the newer concept of embedded scales, we show how one can develop synthetic sustainability indicators, without aggregating attribute scores, through composite indicators. In particular, the paper shows how rankings of countries can be obtained out of multidimensional data systems, paving the way to more comprehensive sustainability studies, where the illustrated posetic methodology, and other tools from partial order theory, can be employed fruitfully. While setting the stage for the application of partial order theory, we also show the use of tools for dimensionality reduction, namely Non-negative Matrix Factorization, which to our knowledge is not yet so widely employed in environmental data analysis.
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