A characterization of a class of border continuous triangular conorms

Let $T^{\ast }:[0,1{]}^2\to [0,1]$ be a continuous, non-decreasing and associative function with neutral element, $f:[0,1]\to [0,1]$ be a strictly monotone function and $f^{(-1)}:[0,1]\to [0,1]$ be the pseudo-inverse of $f$. This article characterizes the function $T:[0,1{]}^2\to [0,1]$ defined by $T(x,y)=f^{(-1)}(T^{\ast }(f(x),f(y)))$ when it is a border continuous triangular conorm.