Abstract
In order to aid in transition towards operations that promote sustainability goals, researchers and
stakeholders use sustainability assessments. Although assessments take various forms, many utilize di-
verse sets of indicators that can number 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 assess-
ment results. Although the choice of aggregation function is a key component in the development of the
assessment, there are few examples to be found in literature to guide appropriate aggregation function
selection. This paper develops a connection between the mathematical study of aggregation functions
and 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, multi-
ple site multiple indicator aggregation, and the determination of error bounds in aggregate output for
normalized and non-normalized indicator measures.