\begin{definition}[Definition:Fuzzy Intersection]
Let $\textbf A = \left({A, \mu_A}\right)$ and $\textbf B = \left({B, \mu_B}\right)$ be fuzzy sets.
Then the '''(fuzzy) intersection''' of $\textbf A$ and $\textbf B$ is denoted $\textbf A \cap \textbf B$.
It is defined to be the fuzzy set such that:
* The domain of $\textbf A \cap \textbf B$ is $A \cap B$.
* The membership function of $\textbf A \cap \textbf B$ is:
::$\forall x \in A \cap B: \mu_{A \cap B}(x) = \operatorname{min}\left({\mu_A(x), \mu_B(x)}\right)$
where $\operatorname{min}$ is the min operation.
\end{definition}