The modularity condition for uninorms and t-operators

In this work we study the functional equation given by the modularity condition F(x,G(y,z))=G(F(x,y),z) for all z ≤ x, where the unknown functions F, G are uninorms and/or t-operators. We characterize all the solutions in the four possible cases: (i) when F, G are t-operators, (ii) when F is a t-operator and G a uninorm, (iii) when F is a uninorm and G a t-operator and, finally, (iv) when F, G are uninorms.