Conic aggregation functions

Inspired by the notion of conic t-norms, we introduce conic aggregation functions. Such aggregation functions are completely characterized by their zero-set. Special classes of binary conic aggregation functions such as conic quasi-copulas and conic copulas are considered. We provide the necessary and sufficient conditions on the boundary curve of the zero-set of a conic aggregation function to obtain a conic (quasi-) copula and conclude that the class of conic copulas is a proper subclass of the class of conic quasi-copulas. Moreover, we characterize the class of singular conic copulas. We investigate some aggregations of conic (quasi-) copulas. Some examples are also provided.