On a new construction of 1-Lipschitz aggregation functions, quasi-copulas and copulas

A new method of constructing 1-Lipschitz aggregation functions is proposed and studied. As a by product, a new method of constructing (quasi-)copulas from a given (quasi-)copula C is obtained. Newly constructed copulas are negative quadrant dependent for any original copula C. The only invariant copula under this construction is the Fréchet–Höffding lower bound W. The method preserves several important properties of copulas, such as modularity, absolute continuity or symmetry, and commutes with some other constructions, e.g., the construction of survival copulas.