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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.