A practical approach for estimating weights of interacting criteria from profile sets
Aggregating multi-criteria data is an important problem with many applications. Commonly-used additive aggregation methods, such as the weighted arithmetic mean, cannot account for the criteria interactions encountered in many practical multi-criteria decision problems. The Choquet integral is a suitable aggregation operator in the presence of interacting criteria. It replaces the weight vector with a fuzzy measure that models the importance of each subset or coalition of criteria, rather than just the importance of individual criteria. However, estimating the fuzzy measures in practice has been problematic. Conventional approaches are cognitively challenging for decision makers, while more recent approaches suffer from prohibitive data requirements. In this paper, we present a formulation for the weights of the Choquet integral that uses principal component analysis to account for criteria interaction. This novel unsupervised approach to estimating the required fuzzy measures overcomes the limitations of other methods. The approach is applied to two case studies in environmental and sustainability analysis, and the results are compared with those of the weighted arithmetic mean. The first case is a triple bottom line analysis of 135 Australian industry sectors evaluated against 11 criteria, while the second case is an environmental life cycle assessment of 8 alternative biosolids management options evaluated against 5 criteria. These examples demonstrate the ability of the proposed approach to account for criteria interaction in these and other decision contexts.