Generalized supremum convolutions on the tensor product of unit intervals: t-conorms and triangle functions

The complete-lattice tensor product $\mathbb{E}=[0,1]\otimes[0,1]$ arises naturally in the algebra of truth values for type-2 fuzzy sets. For a monotone surjective map $S$ that is continuous on $[0,1[^2$ and a monotone map $T$ having $1$ as identity, we consider the generalized supremum convolution