\begin{definition}[Definition:Order Automorphism]
Let $\left({S, \preceq}\right)$ be an ordered set.
Let $\phi: S \to S$ be an order isomorphism from $\left({S, \preceq}\right)$ to $\left({S, \preceq}\right)$.
Then $\phi$ is an '''(order) automorphism'''.
\end{definition}