Ultramodular binary copulas are discussed, i.e., copulas of a random vector whose components are mutually stochastically decreasing with respect to each other. The additive generators of Archimedean ultramodular binary copulas are fully characterized. Finally, a new construction method for binary copulas based on $n$-ary ultramodular aggregation functions is proposed.
Erich Peter Klement. Maddalena Manzi. Radko Mesiar. "Ultramodularity and copulas." Rocky Mountain J. Math. 44 (1) 189 - 202, 2014. https://doi.org/10.1216/RMJ-2014-44-1-189