Aggregation with dependencies: Capacities and fuzzy integrals

We outline recent trends in capacity-based aggregation in large universes. Capacities (fuzzy measures) model dependencies among the inputs, and aggregation by the discrete Choquet, Sugeno and other fuzzy integrals accounts for synergies and redundancies. For large number of inputs the exponential complexity of all interactions is a major obstacle. We exemplify the need for aggregation of a large number of dependent inputs on several applications and discuss the challenges and approaches to reducing the complexity of capacity-based aggregation. We also state which mathematical and computational tools are required for large scale capacity modelling. © 2021 Elsevier B.V.