Aggregation Function Constructed from Copula

In this work, we show that a slight change in the Sklar’s formula tremendously affects the class of aggregation functions it represents. While the original formula can only be used to construct -increasing
aggregation functions, this new formula can be used to construct any continuous aggregation function excepted possibly those belong to the boundary of this set. In particular, all continuous aggregation
functions can be approximated by aggregation functions in this form. This shows that it is sufficient to only consider aggregation functions in this form for most cases. Construction examples via this method
are also given.