The Ordered Modular Averages
Ordered modular averages (OMAs) generalize ordered weighted averages operators, with the replacement of the additivity property by the modularity. OMAs can be seen as a symmetrized idempotent modular aggregation functions, characterized by comonotone modularity. Each OMA can be seen also as a copula-based integral with respect to a symmetric capacity. Special OMAs are characterized, such as associative operators, operators with neutral element, or operators with an annihilator. Some construction methods for OMAs are also discussed.
modularity comonotone modularity symmetric capacity copula