Indicators for the characterization of discrete Choquet integrals

Ordered weighted averaging (OWA) operators and their extensions are powerful tools used in numerous decision-making problems. This class of operator belongs to a more general family of aggregation operators, where each operator of this family is understood as a discrete Choquet integral. Aggregation operators are usually characterized by indicators. In this article four indicators usually associated with the OWA operator are extended to the discrete Choquet integral: namely, the degree of balance, the divergence, the variance indicator and Rényi entropies. All of these indicators are considered from a local and a global perspective. Linearity of indicators for linear combinations of capacities is investigated and, to illustrate the usefulness of results, indicators of the probabilistic ordered weighted averaging (POWA) operator are derived. Finally, a numerical example is provided to discuss the results in a specific context.