Uncertainty

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.