On some construction methods for 1-Lipschitz aggregation functions

Flipping method for constructing copulas from a given copula is extended to aggregation functions. Aggregation functions admitting flipping method are characterized and studied. Moreover, the algebraic structure of several kinds of dualities on aggregation functions, including the flipping method, the reverse method and the standard duality, is classified. Based on composition of construction methods, several new construction methods for 1-Lipschitz aggregation functions are introduced, and their algebraic relationships are studied.