Definition:Fuzzy Intersection

Definition
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.