The distributivity condition for uninorms and t-operators

In this work we study the functional equation given by the distributivity condition: F(x,G(y,z)) = G(F(x, y),F(x,z)) for all x,y,z is an element of [0,1], 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. (C) 2002 Elsevier Science B.V. All rights reserved.