If \\(X\\) and \\(Y\\) are sets with preorders, you can define a preorder on \\(X \sqcup Y\\) by \\(a \leq b\\) iff \\(a \leq b\\) in \\(X\\) or \\(a \leq b\\) in \\(Y\\). This should be the coproduct in the category of posets. This is like putting \\(X\\) and \\(Y\\) right next to each other.

Another preorder on \\(X \sqcup Y\\) is given by taking the one above and adding in \\(a \leq b\\) whenever \\(a \in X\\) and \\(b \in Y\\). This is like putting \\(Y\\) on top of \\(X\\).

Another preorder on \\(X \sqcup Y\\) is given by taking the one above and adding in \\(a \leq b\\) whenever \\(a \in X\\) and \\(b \in Y\\). This is like putting \\(Y\\) on top of \\(X\\).