\begin{definition}[Definition:Inclusion Ordered Set]
Let $\left({S, \preceq}\right)$ be an ordered set.
$\left({S, \preceq}\right)$ is '''inclusion ordered set''' {{iff}}
:$\mathord\preceq = \mathord\subseteq \cap \left({S \times S}\right)$
That means,
:$\forall x, y \in S: x \preceq y \iff x \subseteq y$
\end{definition}