Sustainability assessment

One approach to assessing progress towards sustainability makes use of multiple indicators spanning the
environmental, social, and economic dimensions of the system being studied. Diverse indicators have different
units of measurement, and normalization is the procedure employed to transform differing indicator
measures onto similar scales or to unit-free measures. Given the inherent complexity entailed in interpreting
information related to multiple indicators, normalization and aggregation of sustainability indicators
are common steps after indicator measures are quantified. However, it is often difficult for stakeholders
to make clear connections between specific indicator measurements and resulting aggregate scores of sustainability.
Motivated by challenges and examples in sustainability assessment, this paper explores various
normalization schemes including ratio normalization, target normalization, Z-score normalization, and unit
equivalence normalization. Methods for analyzing the impacts of normalization choice on aggregate scores
are presented. Techniques are derived for general application in studying composite indicators, and advantages
and drawbacks associated with different normalization schemes are discussed within the context of
sustainability assessment. Theoretical results are clarified through a case study using data from indicators
of progress towards bioenergy sustainability.

In order to aid operations that promote sustainability goals, researchers and stakeholders use sustainability assessments.  Although assessments take various forms, many utilize diverse sets of indicators numbering anywhere from two to over 2000. Indices, composite indicators, or aggregate values are used to simplify high dimensional and complex data sets and to clarify assessment results. Although the choice of aggregation function is a key component in the development of the assessment, there are fewliterature examples to guide appropriate
aggregation function selection. This paper applies the mathematical study of aggregation functions to sustainability assessment in order to aid in providing criteria for aggregation function selection. Relevant mathematical properties of aggregation functions are presented and interpreted. Cases of these properties and their relation to previous sustainability assessment research are provided. Examples show that mathematical aggregation properties can be used to address the topics of compensatory behavior and weak versus strong sustainability, aggregation of data under varying units of measurements, multiple site multiple indicator aggregation, and the determination of error bounds in aggregate output for normalized and non-normalized indicator measures.