Biconic aggregation functions

We introduce a new method to construct aggregation functions. These aggregation functions are called biconic aggregation functions with a given diagonal (resp. opposite diagonal) section and their construction is based on linear interpolation on segments connecting the diagonal (resp. opposite diagonal) of the unit square to the points (0, 1) and (1, 0) (resp. (0, 0) and (1, 1)). Subclasses of biconic aggregation functions such as biconic semi-copulas, biconic quasi-copulas and biconic copulas are studied in detail.